Washington DC is very different from NYC: I found it was a really agreable city to visit as the streets are not crowded as in NYC, and the entrance to the museums is free. The city appeared to me very peaceful, quiet, and most of all really clean (not garbage everywhere as we are used to in NYC!). In a weekend, I think it is possible to see most of Washington’s touristic places (The Capitole, the Mall, the White House…) and visit some museums. I particularly enjoyed walking along Georgetown streets and canal. As it was particularly hot and sunny when I visited, I also went kayaking on the Potomac rivers (you can rent a double kayak for 21$/hour).
And of course there are also many places to go out by night, especially around the U Street Corridor, but you’d better start partying early, as the bars and club in Washington DC closed much earlier than in NYC!