i've lived in DC for 2.5 years, and am a transplant from central ny, too.
for housing, i'd recommend checking out craigslist:
http://washingtondc.craigslist.org/
i think that if you want to live downtown you might need to get a roommate to live for less than 1000 a month.
i used to ride in some really rural areas up in central ny, so i was shocked at how much traffic is down here. that being said, if you know where to look, you can find some pretty good rides. without a car, though, to get you to the start of some of these rides, the choices are a lot more limited. you can also go out and ride in the blue ridge, which is a lot more vertical than just about anywhere in central ny.
the pptc website suggested above has some great rides listed, and if you join the club and go to group rides, there are even more rides that they don't have listed. also, you can check out this site:
www.bikewashington.org
the rides i like the most on bikewashington.org are these: Peach Tree Loop, Mason-Dixon-Double-Cross, anything near Sugarloaf mountain, the Blue Ridge Challenge and Skyline drive. Most of those are a drive away, though.
In my personal opinion, living nearer to maryland is better for biking options. (and if you like to ski, the closest stuff is in pa, so living to the north is closer to that, too)