DC
Dupont Circle is good, but make sure you're going to the right bar for you. Under the Front Page (great for Thursday nights) is Buffalo Billiards which is a pretty cool hangout. West of the Circle on O street is Pizzeria Paradiso, highly recommended. A few blocks south on Connecticut Ave is a bunch of popular clubs. Also, take a walk from Dupont to Adam's Morgan (walk up 18th St. to Columbia Rd.), there's plenty of good places there... Crush, Reef, Heaven, Hell, Angry Inch, Madam's Organ, etc. On the way you can stop at Lauriol Plaza on 18th and S for some awesome Latin food. Don't forget a late night jumbo slice of pizza from one of the local joints scattered about 18th St.
Off the Cleveland Park Metro there are a few good spots. (You'll be in the middle of it when you exit the station)
Virginia
Old Town Alexandria has some good spots along King Street. Also, there's always Clarendon for Whitlow's on Wilson and others. I'm sure you'll have plenty to do.
As for what to avoid... I'd avoid everything in the district except for NW (even then don't go as far east as 10th above M street) and Georgetown.
One more thing... take Metro and beware of the time Metro closes, unless you don't mind paying for a cab. On weeknights(Sun-Thurs), Metro closes at 12 am. On weekends(Fri and Sat), it closes at 3am. This is all subject to change based on events in the city.