The best area in my opinion to stay is DuPont Circle. It is on the red line of the metro, there are restaurants and shops everywhere...its just really close to everything. Keep in mind that in DC on weekdays it is really difficult to find a hotel, so I recommend booking soon...if there is nothing around DuPont and all is booked (very possible...happens all the time) other areas with easy metro access are Crystal City, Pentagon area (around Pentagon mall and Pentagon Sq.), Woodland Park, Capital Hill area (dependin where though). I guess usually in DC the goal is to stay anywhere close to the metro, easiest way of transportation there.
To see...the standard tourist sites. All the Smithsonians are great, there is an ice skating ring by the National Museum of Art that is usually fun...Take a walk down Massachusetts Ave toward Maryland, its called Embassy Row..usually a nice pleasant walk and all the embassies. Georgetown is really great. There is a blue bus that goes from DuPont (there is no metro at Georgetown) use to be $1 and it gets you in the heart of Georgetown (ask at your hotel, they will know). Chinatown is now great, filled with great restaurants and bars and actually some nice hotels like Hotel Monaco.
Good luck.
