D-man put together a very good list. I can't recommend a dinner at the Old Ebbitt Grille enough. We're considering hosting our wedding reception there, it is so nice.
Also, drinks on the roof of the Hotel Washington is a great suggestion.
I am also a big fan of Old Town Alexandria...it's like Georgetown, minus the overwhelming crowds. The Torpedo Factory in Old Town is very cool--it used to be an honest-to-God Torpedo facotry, but about twenty years ago the city purchased it and converted it into an community arts space. There's probably 50-60 artists of all types who have studios there, everything from painting to photography to sculpture, to some more bizarre things...it's a good way to kill a couple of hours. And there are some great restaurants/shopping there as well, plus a great promenade along the shores of the Potomac. (Of course, it can get quite chilly during the winter so you might want to skip the riverwalk.)
Other good neighborhoods for strolling/eating/shopping/drinking are Dupont and Adams-Morgan. A-M has a great variety of ethnic restaurants of all types, and a nice urban vibe. Dupont is more trendy, but home to some fantastic restaurants as well. If you like to read, two bookstores that I highly recommend--Kramerbooks in Dupont and Politics and Prose on Connecticutt Ave in the Van Ness neighborhood. I could spend hours at each.
If you're looking for a good nightspot, there's a terrific jazz club in Georgetown called Blues Alley. You often have to get reservations, but the atmosphere in the club is great. There's a fun Irish Pub that I'm partial to in Alexandria called Murphy's...and I'm not sure where you'll be staying, but if you happen to be in suburban Maryland, in Rockville there is a great Italian place called Timpano's that has one of the most fun bars in the area. It's very cozy, and the people watching is great. If you stop by on Friday evening you'll probably catch me and my fiancee lounging on one of the couches next to the fire.
Of course, there's plenty of the normal touristy-type stuff you can do. Something that gets overlooked by a lot of visitors to D.C. is a guided tour of the Library of Congress. It's such a gorgeous building, and their collection is truly extraordinary. The Spy Museum in Chinatown is a bit pricey but a lot of fun--I spent 4 hours there and didn't get bored. And if the weather isn't too cold, my absolute favorite view of D.C. is taking in a sunset fro the steps of the jefferson memorial, overlooking the Tidal Basin.
Dunno if this is what you're looking for or not, but these are my personal recommendations. Have fun.