Map from Google - Bolivia

In Bolivia there are different types of climate depending on area and altitude. In plains and lowlands, the climate is equatorial in the far north and tropical in the centre and south, while in the plateau and the Andean mountain peaks, it's colder and generally quite arid.
Bolivia lies in the Southern Hemisphere, albeit at tropical latitudes, so its seasons are reversed in comparison with the Northern Hemisphere.

Areas with an equatorial climate
The northernmost area of Bolivia (Department of Pando, and northern parts of the departments of Beni and La Paz) is covered by rainforests, and has a nearly equatorial climate: hot and humid all year round, with little variation in temperature, just a few of degrees, from 23/24 °C (73/75 °F) in the coldest months to 27 °C (81 °F) in the warmest months, abundant rainfall, more than 1,500 millimetres (60 inches) per year, and a short dry season from June to August, when less than 50 mm (2 in) of rain per month fall. The rains are most abundant from November to March.
Here is the average precipitation in Cobija, in the far north, near the border with Brazil.
Average precipitation - Cobija
Prec. (mm)265250235185802525451001652201551850

The best time to visit this area runs from June to August, which is not only the driest, but also the least hot: in the daytime it's as hot as in the rest of the year, around 31/32 °C (88/90 °F), but at night the temperature usually drops slightly below 20 °C (68 °F), besides moisture is a bit lower, so the heat is more bearable. However, from mid-August to mid-October, before the rainy season, the temperature increases and the hottest time of the year occurs.
Here are the average temperatures in Cobija.
Average temperatures - Cobija
Min (°C)222121201817161719212121
Max (°C)313131312930313334323131
Min (°F)727070686463616366707070
Max (°F)888888888486889193908888

In Cobija, the sunshine amount is good in the dry season, and in any case decent in the rainy season, given that the rains occur in the form of shower or thunderstorm, and do not last long.
Sunshine - Cobija
Sun (hours)666777887776

Climate of the savanna - Chaco
In the rest of the plains and the lowlands, we find the Gran Chaco, a region which also includes southwestern Mato Grosso in Brazil, western Paraguay and northern Argentina, and which is covered by a savannah-type vegetation. Here the climate is tropical, with a dry season in winter, and a wet season in summer. During winter, the temperature drops by a few degrees, especially in the centre and south: the average temperature in June and July is 23 °C (73 °F) in Trinidad, 20 °C (68 °F) in Puerto Suarez, and drops to 16/17 °C in the extreme south, also due to the altitude that in this area is higher, on average around 600/700 metres (2,000/2,300 feet). As typically happens in the tropics, this area is hottest in spring, before the rain season, so that heat spikes, from 37 to 40 °C (99 to 104 °F) are recorded from September to November. Then the summer, albeit less hot, is sultry, therefore in this season the heat is still uncomfortable.
The rains are more abundant in the western part, near the eastern range (Cordillera Oriental) of the Andes: along the northeast facing slopes at the foot of the Andes, there is no real dry season, because even in winter some showers are possible (see San Buena Ventura).
Here is the average precipitation in Santa Cruz de la Sierra, located in the central part, at 400 metres (1,300 feet) above sea level.
Average precipitation - Santa Cruz
Santa CruzJanFebMarAprMayJunJulAugSepOctNovDecYear
Prec. (mm)20013012011090706040701001201701280

In the southern part, south of Santa Cruz de la Sierra, the climate tends to become more arid: the annual rainfall is lower than 1,000 mm (40 in) per year, and in addition the dry season becomes longer, since it goes from May to September instead of June to August, as happens in the north-central. In this southern area, being further away from the Equator, thermal variations also increase: from September to November, the temperature can reach 40 °C (104 °F), while between May and August at night it can drop even to the freezing point (0 °C or 32 °F).
In fact, the central and southern part of the region, during winter, from May to August, are affected by sudden drops in temperature, due to cold winds blowing from the Argentinian Pampas, called Surazos. In Santa Cruz de la Sierra, the night temperature may fall between 5 and 10 °C (41 and 50 °F), but sometimes even below 5 °C (41 °F), especially in June and July. In the south, night minima can drop at times as low as a few degrees below freezing. Cold winter outbreaks are short, nevertheless they are significant for the latitude (we are still north of the Tropic of Capricorn). Here are the average temperatures in Santa Cruz.
Average temperatures - Santa Cruz
Santa CruzJanFebMarAprMayJunJulAugSepOctNovDec
Min (°C)212120191615151619202021
Max (°C)303030282523242829303131
Min (°F)707068666159596166686870
Max (°F)868686827773758284868888

In Santa Cruz the amount of sunshine is good enough all year round, and reaches its peak in August, that is, in the driest month and at the end of winter.
Sunshine - Santa Cruz
Santa CruzJanFebMarAprMayJunJulAugSepOctNovDec
Sun (hours)777877798887

Climate of the Andes in Bolivia
The Andean area is delimited by two cordilleras, between which there is a plateau where you will find the capital and other major cities of Bolivia. The western cordillera is much less rainy than the eastern one. The plateau is fairly barren, and in the south-west, near the border with Chile, it becomes even desert. In the Andean region there are high mountains, such as the volcano Sajama, 6,542 metres (21,463 feet) high, Janq'u Uma, 6,427 metres (21,086 ft), Nevado Illampu, 6,368 metres (20,892 ft), and Illimani, 6,402 metres (21,004 ft).
Winter in the high mountains is dry, however, brief snowfalls are possible above 4,000 metres (13,000 ft) in winter and early spring. The snowline is very high, above 5,000 metres (16,400 ft), because of the scarcity of snowfall in the coldest season.
In general, in the plateau the diurnal temperature range is high, and after the sunset the air cools quickly. Being the air dry, the cold is more bearable, except when the wind blows.

Cable car La Paz - El Alto

The capital of Bolivia, La Paz, is located at an average altitude of 3,600 metres (11,800 ft), so it is the highest capital in the world, but the various districts are located at an altitude between 3,200 and 4,100 metres (10,500 and 13,500 ft), so there are different temperatures from area to area. The airport is located in the highest area (El Alto), at 4,050 metres (13,300 ft) above sea level: in this part of the city, the climate is cold all year round: the average daily temperature goes from 5 °C (41 °F) in June and July, to 9 °C (48 °F) in November (which is, albeit slightly, the warmest month, because in summer, rains and clouds are able to lower the temperature a little). At the airport, night temperatures easily drop below freezing in the coldest months, from May to September, with peaks of -10 °C (14 °F), while during the day the temperature becomes fairly mild, 12 to 15 °C (54 to 59 °F). Sometimes it can even snow, as happened on July 4, 2015, more significantly in the upper part of the capital, as well as in other cities placed at very high altitudes such as Oruro. In the summer months, the temperature does not rise by much, just a few degrees.
Here are the average temperatures recorded at the airport.
Average temperatures - La Paz
La PazJanFebMarAprMayJunJulAugSepOctNovDec
Min (°C)33320-2-2-10233
Max (°C)121313131312121313141514
Min (°F)373737363228283032363737
Max (°F)545555555554545555575957

The total annual rainfall is around 560 mm (22 in), but since there is no warm month in which trees could grow, here tundra dominates, like in sub-polar areas. The rains fall mostly from September to April, with a peak from December to March, when they are more frequent (up to 20 days per month), and can sometimes be abundant, causing floods and landslides. Here is the average precipitation.
Average precipitation - La Paz
La PazJanFebMarAprMayJunJulAugSepOctNovDecYear
Prec. (mm)120100703010551030405090560

The sunshine amount is good from May to August, while it is not very good in the rainy season, when there can be morning mists as well.
Sunshine - La Paz
La PazJanFebMarAprMayJunJulAugSepOctNovDec
Sun (hours)655689987666

At lower elevations, in the central area of the city, which is located at 3,650 metres (11,975 feet), the temperature is higher by a few degrees, and that's something, since during the day it reaches 14 °C (57 °F) in winter and 15/17 °C (59/63 °F) in November and in the summer months; in the lowest neighbourhoods, situated just above 3,000 metres (10,000 ft) of altitude, the temperature rises to 17/19 °C (63/66 °F), and winter frosts, when they occur, are light.
Here are the average temperatures of the low part of the city, at 3,250 metres (10,650 ft) above sea level.
Average temperatures - Lower La Paz
Lower La PazJanFebMarAprMayJunJulAugSepOctNovDec
Min (°C)666431123466
Max (°C)171718181817171718191918
Min (°F)434343393734343637394343
Max (°F)636364646463636364666664

The best time to visit La Paz goes from May to August, though it's the coldest, because it's also the driest and sunniest.

Lake Titicaca

West of La Paz, at no great distance from the capital, we find Lake Titicaca, which is the highest navigable lake in the world, being located at 3,800 metres (12,500 ft) above sea level, while to the south we find the archeological site of Tiwanaku, located at the same altitude. This area has a climate similar to that of the highest part of La Paz, but often with a higher temperature range, so that, while during the day the air is mild, in the evening, especially in winter, the temperature falls rapidly after sunset, and at night drops below freezing.
Here are the average temperatures of Tiahuanaco (or Tiwanaku).
Average temperatures - Tiwanaku
Min (°C)4441-2-5-5-40134
Max (°C)161515151414131415171816
Min (°F)393939342823232532343739
Max (°F)615959595757555759636461

The other capital, Sucre, is located further south, at an altitude of 2,800 metres (9,200 ft). Compared with La Paz, here the temperatures are higher, that is, spring-like all year round, but at night it is often cold in winter, since lows hover between 5/6 °C (41/43 °F) in the June-August period, and 11 °C (52 °F) from November to March, while the daytime temperatures hover around 22/24 °C (72/75 °F) throughout the year. Here are the average temperatures.
Average temperatures - Sucre
Min (°C)111110975568101111
Max (°C)222222222222222324242423
Min (°F)525250484541414346505252
Max (°F)727272727272727375757573

In an average year, 680 mm (26.5 in) of rain fall. Summer is the rainiest season here as well, therefore the best time is winter, from May to August.
Here is the average precipitation.
Average precipitation - Sucre
Prec. (mm)1551151053062212255065120680

In Sucre too, the amount of sunshine is better in the dry winter season than in the rainy summer season.
Sunshine - Sucre
Sun (hours)567788898776

In Cochabamba, located at 2,500 metres (8,200 ft) above sea level, the temperatures are slightly higher. Here, daytime temperatures fluctuate throughout the year between 23 and 26 °C (73 and 79 °F), but the diurnal temperature range is high, so the nights are cold from May to August.
Average temperatures - Cochabamba
Min (°C)1312121063369111213
Max (°C)232323252423232425262625
Min (°F)555454504337374348525455
Max (°F)737373777573737577797977

In Cochabamba, rainfall amounts to only 550 mm (21.5 in) per year, and the dry season is very long; the rains are substantial only from December to March. Here is the average rainfall.
Average precipitation - Cochabamba
Prec. (mm)1351108025624813254595547

Also in Cochabamba, the sun shines more often in the dry season than in the rainy season.
Sunshine - Cochabamba
Sun (hours)566788898766

In the southwest, near the border with Chile, the plateau becomes definitely desert. Here we find Salar de Uyuni, a huge expanse of salt, located at 3,650 metres (12,000 feet) of altitude, where the tropical mountain sun, already strong, increases its effects due to reflection on the white surface: better to bring sunglasses and sunscreen. Being arid, this area doesn't have particular problems as regards the weather, and can be visited throughout the year, though it's preferable in summer, when the temperature is higher.
Here are the average temperatures of Uyuni, located at 3,650 metres (12,000 feet) above sea level; as you can see, from May to September at night the temperature falls, and normally drops below freezing. Here, just 145 mm (5.5 in) of rain per year fall, concentrated from November to March.
Average temperatures - Uyuni
Min (°C)4431-3-6-6-5-2124
Max (°C)171616171514131516171817
Min (°F)393937342721212328343639
Max (°F)636161635957555961636463

When to go

The best time to visit Bolivia in its entirety runs from June to August: even though at high altitudes it's the coldest period, it's also the least hot at low altitudes, and above all it's the driest and sunniest throughout the country.

What to pack

In winter (June to August): in the forest, lightweight clothing of natural fibres, maybe with long sleeves for mosquitoes, a sweatshirt for the evening. In the savannah, light clothing, a sweatshirt or sweater and a jacket for the evening, especially in the south. In the Andes (La Paz, Lake Titicaca), clothes for spring and autumn for the day, and warm for the evening: warm jacket, warm windproof hat; sunglasses, sunscreen. In the high mountains, warm clothes, down jacket, scarf, gloves, hiking boots.

In summer (December to February): in the forest and the savannah, lightweight clothing, possibly a light sweatshirt and a light raincoat for thunderstorms, sun hat. In the Andes (La Paz, Lake Titicaca), clothes for spring and autumn, raincoat or umbrella, jacket, sweater, sunglasses, sunscreen. In the high mountains, warm clothes, down jacket, scarf, gloves, hiking boots.