Edinburgh also has an exchange to Georgetown and for whatever reason it's the most expensive for accommodation of all of the uni exchanges offered. Even more than California, which I found surprising.
I just returned from visiting the uni, but for biology/biochem not social sci. The uni campus is very nice pretty much contained and small, and it's located in a really "yuppy" /"preppy" part of town. I wasn't looking really hard (not enough time), but I didn't see any clubs, pubs, etc. that seem to be part of student life in the UK. Drinking age is 21, maybe that has something to do with it. I'm not a party animal, but enjoy going out to hear new bands etc from time to time.
If you're into museums at all Washington has the most amazing Smithsonian museums - could spend hours wandering around there...
Also not much to do in the winter if you're a sports fan.. I love skiing, snowboarding etc. don't know where the nearest ones are but certainly not 1-2 hrs away that you could go for the day.
Weird thing is for the 3 days I was there all I heard were sirens all day long.. police, fire trucks, ambulances, helicopters and Bush wasn't even in Washington he's at the G8 summit. Cameras everywhere, and even walking into the hotel security will stop you and sometimes search your bags at random.