Let me (or us) know if you find a place to live! This is a great place to spend 8 weeks. What exactly will you be doing? If you would rather tell me via PM, that's cool.
Here is the map for the Metro, so you can see where areas are.
http://www.wmata.com/metrorail/systemmap.cfm
Capitol South takes you to right outside the Cannon House Office Building, which is right next to the Capitol. The Senate House Office buildings can be accessed through an underground tunnel system, but would be no more than a 10-minute walk. You can also get to the Senate via the Union Station Metro Station on the Red Line.
Capitol Hill is a great area. The architecture is stunning, and you have restaurants on both sides of Congress (House on South side, Senate on North side). Union Station is the coolest place. That's close to the Senate office buildings. There are restaurants, stores, you name it. And it is gorgeous inside.
Arlington, Virgnia, is also great. There are places to live by the following Metro stops, and each place has restaurants, stores, etc--Rosslyn, Courthouse, Clarendon, Virginia Square, and Ballston. Any of those places would be great and all are on the Orange Line, except for Rosslyn which is on both the Orange and Blue Lines. Both of those lines go directly to Capitol Hill.
Georgetown, while very cool, isn't close to a Metro station, but it's not too far from the Foggy Bottom Metro Station. I love Georgetown, although the sidewalks are a little too narrow, but it has everything you could ever want for shopping and eating.
Alexandria is also cool, although I am not as familiar with that area as I am the others. Old Towne is very similar to Georgetown with places to shop and eat, and the atmosphere is beautiful and just totally cool. I think the Metro stations in that area are Braddock Road and King Street.
Pentagon City has recently been improved and has places to live and places to eat. The Pentagon City Mall is there, and that mall is 3 stories high with a ton of stores. It's a great location as well. Chrystal City is just okay. I don't think it has the pizzaz that the other locations have.
Bethesda, Maryland is also a great location--restaurants and stores galore.