Easiest place to stay is the apts across the street from the hospital; generally you should be able to get a studio or 1 bedroom; occasionally you might have to share a 2-bdrm with another studio. I don't think it's very safe to live anywhere else in Bridgeport but there are very safe areas just 15 min away by car. The apts across the street are furnished and have laundry machines in the basement.
There is basic cable, but no internet. If you are staying for longer however, you can sign up for internet service but you first need to get permission from the clerkship coordinator (because she maintains the apts). I would not recommend doing that however (PM me if u need more info regarding this). My suggestion would be to sign up for some sort of wireless internet service through ATT/sprint/verizon.