I LOVE D.C. I lived there for four years....
There are a few things that are really worth spending money on. There's a trolley tour of the city that goes to all the monuments. You can buy a day pass and then get on and off at any point along the route. It's a MASSIVE time and foot saver to see all the monuments and Arlington Cemetary. Definitely worth spending a day doing this. Of course, don't miss the Vietnam memorial, one of my favourites. It's simply overwhelming to see all those names....
The Air & Space Museum (Smithsonian) is my personal favourite - but check out the other ones to see what exhibits are on and then choose your favourite. Don't try to go to too many...it's overwhelming!
Spend some time in Georgetown, perhaps check out a night club or two, and have a coffee at one of the cafes and perhaps dinner.
Speaking of dinner, try to get into one of the posh downtown dinner spots - you'll be amazed at who you'll see dining out!
That should keep you busy to start with!