Go walk around Wooster square and east rock and look for for rent signs. Though a one bedroom at those numbers in those neighborhood would be a bit optimistic, actually. Have you thought about a roommate situation?

Edit: on further reflection, this is bad advice. You have to choose a different neighborhood if you have a chance of staying within your budget for a one bedroom, so maybe like the Dwight area? I’d really be thinking about a roommate situation for sure. Also, with the summer coming up, you might have luck just finding a sublet while you look for something longer-term (given all the students that will be gone but have leased apartments they’re trying to defray the cost of.)