NeedMoving to DC. Any friendly neighbors with good advice?

Hi, I'm moving from Miami to DC in December. I've been accepted to grad school at American University. And I'm totally lost as to where to begin lookin for housing. I've been told city apartments are just as expensive as the suburbs. I just need to find a nice decent place close to AU. Maybe in the range of a $1200 1 bedroom apt. Being from Miami, I'm used to the proximity to shopping centers, banks, supermarkets when chosing a place to live. Definitely would take that into consideration for DC as well. Another thing is, I'm bringing my car. I've been told I probably won't be needing it much. It's a 2007 VW Jetta. Will I be needing winter tires? or some special service for it to survive in the new weather?

Any advice would be greatly appreciated.