Map from Google - Washington

The climate of Washington, D.C. (District of Columbia), the US federal capital, is semi-continental, with cold winters, sometimes snowy, and hot and muggy summers. The city is located at the 38th parallel, a little half-way between the cold and the warm half of the United States. In winter it can be affected by cold air masses coming from Canada, but less frequently than in New York; in summer the heat is felt, with long periods of sunshine and hot weather, but also with salutary afternoon or evening thunderstorms that come to temporarily break the heat.
Here are the average temperatures of the Reagan National Airport, a few kilometres south of the city center, in Arlington County, Virginia; here a mild microclimate is found, because of the Potomac river that widens becoming almost a lake, so lows are a couple of degrees higher than in peripheral areas and in the surrounding countryside.
Average temperatures - Washington
Washington J F M A M J J A S O N D
Min (°C) -2 -1 3 8 14 19 22 21 17 10 5 0
Max (°C) 6 8 13 19 24 29 31 30 26 20 14 8

Precipitation in Washington is quite abundant, since it amounts to about 1,000 millimetres per year, and is well distributed throughout the year. In summer, the rains occur, as well as for the passage of some disturbances, mainly because of afternoon or evening thunderstorms.
Here is the average precipitation.
Average precipitation - Washington
Washington J F M A M J J A S O N D Year
Prec. (mm) 70 65 90 80 100 95 95 75 95 85 80 75 1005
Days 10 9 11 10 11 11 10 8 8 8 9 10 114

Winter, from December to February, is cold: the average temperature is just above freezing. At night, light frosts occur frequently, or lows around zero degrees, while during the day the temperature typically exceeds freezing by a few degrees. The weather is unstable, so that sunny days alternate with rapid outbreaks of cold air, with snowfall and temperatures around freezing; in these situations the wind can exacerbate the feeling of cold. In a year, an average of about 40 centimetres of snow falls (while in the Dulles Airport, actually located 37 km north-west of the city, in the state of Virginia, snowfall arrives at 65 cm). Big snowstorms, which can block or slow down many activities, called Snowmageddon, occur on average every 4/5 years. During the most intense cold waves, in which the temperature remains below zero degrees even during the day, lows can plunge to -15 °C, and sometimes even -20 °C.
However, there may also be a day, or periods of a few days, particularly mild, in which the temperature can touch 15 degrees, and sometimes even 20 °C, which confirms the instability of the climate of Washington and in general of the American East Coast.

In spring, from March to May, the weather continues to be unstable: the first warm days alternate to the return of the cold. In March it can still snow, and sometimes this can also happen in early April. But already in April sometimes the temperature can exceed 25 degrees.
The National Cherry Blossom Festival lasts three weeks and starts on the last Sunday of March (ending therefore in mid-April), when the cherry trees from Japan, donated at the beginning of the 20th century by the mayor of Tokyo, are in bloom.
In May, by now the average temperatures are pleasant, although there are still cool and rainy days, especially in the first half, while the first heat waves can bring the temperature above 30 degrees. On sunny days, also the first afternoon thunderstorms can erupt.

Summer, from June to August, is hot and muggy, especially in July and August. The days with pleasant temperatures, around 25/27 degrees, maybe even rainy, are possible, but more often there are hot and sultry days, with highs around 30 degrees. There may also be heat waves, which can last a week, and in which the daytime temperature can reach or exceed 35 degrees, and even the night temperatures remains high, around 25/26 degrees. More rarely, as in July 2012, temperatures can touch 40 °C. The sunshine amount during the summer is good, even though, in addition to the passage of some disturbances, which can bring clouds and rain, in fine weather thunderstorms may break out in the afternoon.

Autumn, from September to November, is the mildest season of the year and the less unstable, at least in the first part. In the first half of September the weather is often still characterized by heat and humidity, with sunshine and some afternoon thunderstorms, then it becomes milder and relatively quiet until mid-October, while the second half of October can start to be a bit cold. November is by now a cold month, in which the first snowfalls can occur. The rains are not lacking even in autumn, but this is still the season when the rains are a little less frequent.

The amount of sunshine in Washington is good in summer, but it is not scarce even in winter, because as mentioned some sunny days can always occur. On average, there are 9.5 hours of sunshine per day in June and 9 July, and 4/4.5 in December and January.

Lincoln memorial from above

For swimming, the sea along the coast to the east of Washington, in the Chesapeake Bay (see Chesapeake Beach, Annapolis), about an hour's drive from town, is a bit warmer than on the Atlantic Coast (see Dewey Beach, Ocean City), where in summer the temperature is around one degree lower.
Here is the average sea temperature in Atlantic City, on the Atlantic coast, a little north of Ocean City.
Average sea temperatures - Atlantic City
Atlantic City J F M A M J J A S O N D
Sea (°C) 6 4 4 6 11 17 22 23 21 17 13 9

When to go

The best periods to visit Washington are spring and autumn, to avoid both the winter cold and the summer heat, and in particular from mid-April to mid-May, and from mid-September to mid-October. In early September there's often still a sticky heat, though not as intense as in midsummer. In April, sometimes it can get cold and the weather can be unstable, especially at the beginning of the month, while generally the second half of the month is mild.
In autumn (usually around late October) you can admire the beautiful colours of the trees shedding leaves (the phenomenon called fall foliage).