LittleItalyCleveland:
I am not sure what the West Side Market is but in addition to Eastern Market, Union Market (near the Rhode Island Ave metro station -- about 1/3 of a mile, you can also ride the Capital Bikeshare there) opened last summer and it has bee a huge benefit to the city. It is in the warehouse section of DC. Union Market has local, artisanal foods, cheeses, etc. The Rappahonack Oyster Bar is suppose to be very good (although I do not eat oysters).
Here are some photos from our trip there this past spring.
(All photos taken by me).
Here is the link for Union Market:
http://unionmarketdc.com/.
As far as airports, you can take the WMATA 30 bus from BWI to the Greenbelt station (on the Green line). I think the 30 bus runs every half hour and it is about $5 per person. Reagan-National, of course, is the most convenient airport to DC. Dulles is 25 miles west and is reachable via the 5A bus, which goes both to Rosslyn (where you can connect to the Blue/Orange lines) and L'Enfant Plaza. This bus is also $5 and runs approximately every thirty minutes.
As far as things to see/do, if you're going to Eastern Market, check out the Navy Museum on base at the Navy Yard (bring a valid photo ID). This museum is free and is one of Washington's best-kept secrets. While over in that neighborhood, the Yards Park and Riverwalk are also both very nice.
The observation deck at the Old Post Office on Pennsylvania Ave is also worth visiting. I would also recommend visiting either 14th Street (
http://www.washingtonpost.com/local/...211_story.html) and H Street, which has a lot of new bars and restaurants.