Chicago, where it's located

In Chicago, the main city of Illinois, located in the American Midwest, along the banks of Lake Michigan, the climate is continental, with freezing winters and hot summers. Although the city is located at a middle latitude, in winter it is cold because the North American land mass cools down a lot, and polar air outbreaks are frequent. Given the distance from the sea and the exposure to different types of air masses, temperature changes are frequent.
Here are the average temperatures recorded at the O'Hare International Airport.
Chicago - Average temperatures
Min (°C)-9-7-2491518171260-6
Max (°C)-1281521272928241792
Min (°F)161928394859646354433221
Max (°F)303646597081848275634836

Precipitation amounts to 935 millimetres (37 inches) per year, and is well distributed over the seasons, at least in frequency, while in terms of quantity the winter is the driest season. In winter, and in spring and autumn, weather fronts pass, while in late spring and summer, when they become less frequent, thunderstorms can form in the afternoon or evening: it is no coincidence that August is the rainiest month. In winter, precipitation mainly occurs in the form of snow. An average of 92 centimetres (36 inches) of snow falls per year; every once in a while, a snowfall can be seen already in October, and in spring, sometimes it can snow even in April. The record belongs to the winter of 1978-79, when a total of 228 cm (90 in) of snow fell. Here is the average precipitation.
Chicago - Average precipitation

Winter in Chicago runs from late November to early March and is cold, to the point that the average temperature is reminiscent of Northern European cities. But at least here the days are not as short as in the Nordic countries.
Snowfall is frequent, so much so that it snows for several days in a month; sometimes real snowstorms can occur.
Polar cold spells are accompanied by the blizzard, the north wind blowing in gusts and able to heighten the feeling of cold. Particularly cold periods, in which the minimum temperature drops to -20 °C (-4 °F), occur practically every year, and sometimes it can even drop to around -30 °C (-22 °F); for example, in January 1982 the temperature dropped to -32.2 °C (-26 °F), in January 1985 to -32.8 °C (-27 °F), and in January 1994 to -29.5 °C (-21 °F).
Although the temperature remains below freezing (0 °C or 32 °F) even during the day for weeks, sometimes it can exceed freezing also in winter, resulting in melting snow and possible rainfall. Every so often, also the phenomenon called "ice storm" (or freezing rain) can occur, that is, a rain falling on frozen ground, and freezing everything, roads, trees, light poles, cars etc.

Spring, from mid-March to May, is an unstable season, characterized by different situations and temperature changes: initially cold in March, with snowfall and still quite frequent frosts, it advances gradually, between the first warm days and the return of cold weather conditions. In early April it can still snow, on the other hand during the month the first warm days can occur, with highs around 30 °C (86 °F). In fine weather, a cool (or even cold) breeze in the afternoon blows from the lake, which is felt especially in the eastern districts of the city. In May, it can still be cold at night, especially at the beginning of the month, while on other occasions it can be hot, with highs above 30 °C (86 °F). In April and May, on fine warm days, also the first thunderstorms in the afternoon or in the evening can occur.

Summer, from June to August, is hot, humid and sunny, with some afternoon or evening thunderstorms. There may be some pleasant days, with highs around 25/27 °C (77/81 °F) and cool nights, but also real heat waves, with highs around 35 °C (95 °F) and beyond. In the worst moments, the temperature can reach as high as 40 °C (104 °F), as happened in July 2012.

Autumn, from September to November, is the (relatively) quietest period of year. However, we can not rule out early cold weather or the return of warm temperatures, and even waves of bad weather. In early September, the weather is often still characterized by heat and humidity, with sunshine and some afternoon thunderstorms, then it becomes milder. In early October, particularly mild days, even warm, can occur, but in the course of the month there may be slight frosts. Between late October and early November, usually after the first night frosts, a mild period, with highs above 20 °C (68 °F), can occur: it's the so-called Indian summer. However, during the month of November it can get cold, with the first snowfalls and intense frosts.

Chicago skyline and lake

The amount of sunshine in Chicago is very good in the summer, when there are several sunny days, and is good in May and September; in the other months it's not high, especially in November and December, when the sun shows up rarely enough: there are on average 10.2 hours of sunshine per day in July, and 3.4 in December.
Chicago - Sunshine

At Chicago, Lake Michigan is very cold in winter (and on colder winters it can partially freeze, and fully on the coast), while in summer it is still cool, but becomes almost acceptable for swimming, at least in August, or for those who do not suffer from the cold. However, it depends on the period: after a series of some hot days in a row, the lake can become more temperate.
Here are the average lake temperatures.
Chicago - Lake temperature
Temp (°C)43336121921191495
Temp (°F)393737374354667066574841

When to go

The best period to visit Chicago is the beginning of autumn, from early September to mid-October. You can also choose the spring, from mid-April to late May, but it is a more unstable and windy season. However, in both periods you may run into a bit of cold at night, or hot temperatures during the day, or some rainy days. Those who can stand the heat can also choose the summer, which has longer days and more hours of sunshine, but also the risk of very hot days; however, the summer can also give acceptable periods (and maybe even cool nights).