For housing,Craigslist might be your best bet. You could also check out these links:
http://www.google.com/search?hl=en&q=apartment+locator

DC is an expensive town,so getting into a decent neighborhood for $1k/month may require at least one roommate or shoehorning yourself into a crackerbox. Avoid anything in SE(southeast) and don't forget to check VA and MD;we have a pretty extensive Metro system,so you may do better outside the actual district. http://www.wmata.com/ will show you where all it goes.

DC is a good place to ride,you just have to watch the traffic. I was here before in the 90's and it's gotten worse. The drivers don't give a fig about what's going on outside the shell of their car. Keep your eyes open and a finger on your brakes and you should do alright. We usually don't get much snow,so biking year-round isn't a prob. If the weather's too bad to ride,then everything is shut down anyway.

There's lots of gyms around(I always get a kick out of seeing folks drive their SUV's to the health club so they can ride the stationary bikes. ). Get a yellow pages and call around for the best rates.

There's lots of trails around here,althought if you really want to get muddy you'll need to hit the burbs. Everything in the city is paved,gravel,or hardpack. All the dirt trails I've come across didn't allow bikes. The paved trails are MUPs,so they can turn into zoos on weekends,but in the daytime during the week and after the weather cools off they're fine. If you're looking for some truely fun rides,you could always become a Pirate. Check out the "DC Pirates' Pillages and Plunders" thread in the Singlespeed/Fixed forum for our doings and Yahoo list.

Welcome to the District of Columbia. Remember: keep to the right when standing on the escalators!