$800 basement studio apt in a private house (they exist)$900 in a crappy building $1000 ^ in a normal nice building All of that is estimated, and in good neighborhoods, sometimes you can get lucky and get a good apt for your price
If you don t absolutely have to have your own apartment, you could share a 2 bedroom apartment with a roommate for 700-800 in decent parts of town. These are the apartments that are under rent control that new renters would probably have to pay double for now.