I'm currently a 2L at WCL; more than happy to take questions via thread or PM.
Re: neighborhoods. People tend to live all over the city; some tend to live closer to the law school (there are a number of basement apartments and such available) or in Tenleytown, but as someone mentioned earlier, not too many actual apartment complexes around. Folks generally tend to live in Friendship Heights/Chevy Chase, Cleveland Park, Woodley Park, and Van Ness (mostly because of the easy access to the Red Line -- Friendship Heights is also the start of the N4 bus line, which is convenient and drops you off right next to the law school; the N8 goes through Glover Park and also drops you off near the law school, though it doesn't run on the weekends).
Dupont is an option and is in a very lively part of town, but can get quite pricey. Those who want to live closer to the city and closer to nightlife tend to live in AdMo or Columbia Heights, but it's a pain to get to school (AdMo really doesn't have a metro -- closest Red Line metros are Woodley Park or Dupont; Columbia Heights is on the green/yellow line). A few people live further away -- Northern Virginia (Pentagon City, Rosslyn), Capitol Hill, etc. but the commute is a pain. Generally, the further away from the city you go (towards Bethesda if you're going towards Maryland, Rosslyn/Arlington/Crystal City/Alexandria if you're going towards Virginia), the more affordable the apartments will be.
Also, I wouldn't worry terribly about getting housing now. While it's definitely great to meet up with people online and try to coordinate housing that way, it's usually pretty easy to find a place to live/roommates and such. WCL does run its apartment/housing search event over the summer, and AU also has a site of its own
where it has listings for off-campus residences.