Do the metro, it's your best bet. If there is a place you want to go that the Metro doesn't go to, go to the closest Metro station and cab it. Cabs aren't pricey out here, and a lot of the cabbies treat customers well. I wouldn't advise renting a car, parking is a bitch and you pay everywhere you park. Some of the places you'll want to check out:
1. Old Town Alexandria (it's the coolest fucking town, obviously I live here)
2. Georgetown, Washington DC (another cool spot, crowded with tourists at most all times)
3. Baltimore, MD (Inner Harbor rocks, it's fucking awesome if you have 24 hour access to a 45 ft boat in the Harbor, like I do)
4. Annapolis, MD (you get great fucking crab cakes here, ask Jack)
5. Arlington, VA (They have Pentagon City which is a decent mall, The Pentagon, Arlington Cemetery, and all sorts of other cool shit).
6. Washington, DC (There are lots of cool places like U St, National Mall, White House, Museums, etc. You can spend all day here and not get bored if your old and into history and shit.)
These are just some of my opinions, there is a lot to do if you want to venture to some of the outside areas as well.
kneifl