Many trips to Washington are as a stop off on a more comprehensive itinerary seeing more of the country, and often people time their visits to coincide with other places. Having said that, Washington has plenty going on throughout the year, and there will often be some major festival or event on during your stay. The peak tourism season is from April through to September, although many of the hotels offer reduced rates actually in June and July, because the number of business travellers to the city goes down.
Weather wise, the best time to visit is during spring and autumn, when you will find the temperature most comfortable, and the earlier - or later you go, the smaller the queues at the main attractions will be.
