If you're looking for more down-to-earth places to explore, I'd recommend Old Town Alexandria, U St., and H St. NE, in addition to the places others have mentioned.
In Arlington, there are some less-pretentious and less-frat feel places around, but you have to know where to look

Unfortunately Dr. Dremos is no more, as you probably would have liked it. However, there is still the Lost Dog Cafe in Westover, which is not really a "bar" but still a cool place to just chill. Then there's Four Courts and Kitty O'Shea's in Courthouse; two excellent Irish pubs. In Clarendon the Liberty Tavern seems alright, though I haven't really hung out there enough yet to tell if it is getting much spillover from the meat market (i.e., Ballroom) next door. Clarendon Grill is decidedly more relaxed than the Ballroom too. Continental in Rosslyn is a pretty cool pool hall in my opinion, and it usually is not very crowded at all compared to its siblings (e.g. Buffalo Billiards) in the city. If sports is your thing then I suggest Mister Days in Clarendon, the Crystal City Sports Pub, and Summers in Courthouse.