jeanettethierry,
Which websites are you using to find your apts? I'm moving in Jan as well, but all the websites I keep hitting show really expensive choices (~$2k for studio). Granted right under them are the red line metro stops, but I'm willing to walk a few blocks for a less expensive place.
Also -- from my research, Friendship, Cleveland Park, VanNess areas seem really nice for young professionals (or so I've been told). And it seems Cleveland Park/Friendship is the least expensive of them all. Hopefully when I visit the city this coming week I'll find out a lot more. It seems that anything west of the Capitol is safe (depends on what you call safe though). I checked out a website that lists all the murders in the city and there was nothing to the west and roughly 200 to the east. I'm sticking to the west ;-).