The Spy Museum is great. Yup, I think the tickets cost $11. The line gets really long, but it moves quickly. I think Joan Mir?'s painted sculpture is still on exhibit at the Corcoran Gallery and it's pretty interesting. Entrance is $5 and there should be more than one exhibit at a time.
Shopping...it's better to the outlets in Virginia like Potomac Mills. Taxes are lower in VA. I'm not sure if you even have time to go shopping though.
Georgetown is expensive, but an interesting little town.
The shops and apartments are very quaint. Some streets even still have cobble stones and railroad tracks.
A lot of people say it looks very European (I think the place was actually designed by a Frenchman). There are different kinds of restaurants here (French, Italian, Vietnamese, Thai, Chinese, Indian, American, etc., etc.). Take a stroll down the Washington Harbour. There are outdoor bars facing the Potomac River. You can try the Sequoia restaurant there too. BTW, the house where the "The Exorcist" was filmed is here in Georgetown (on M Street). You can also check out the Washington National Cathedral. It's not that old though, so not much history, I think
, but it's nice. There are historic houses too, like the Old Stone House which is right smack in Georgetown. Entrance is free. It's interesting to see it next to the restos and shops. There are also mule-drawn boat rides, which carry park visitors on the C & O canal. There are art galleries in Georgetown too.
Adams Morgan is an ethnic neighborhood. There are lots of bars and restaurants there too. Dupont Circle is great (it reminds me of the Village in NYC). There are shops, small movie theatres, bars, and a nice bookstore called Kramerbooks. This neighborhood's close to the Embassy Row. Like Georgetown, there are a lot of good places there to eat (La Tomate, Teaism, Bistrot du Coin, Raku, etc.).
If you like animals, you can go to the National Zoo at Woodley Park.
Alright, I've rambled. Anyway, if you have any questions or wanna meet up, just PM me.
Have fun!