I just joined trulia and noticed nobody had answered this yet so maybe I can help. Could you provide a little more info on what hospital you are referring to? I'd be happy to help you search rental properties and see what's out there in your price range. Or if you want to look, you can search craigslist, hotpads, rent.com, and other rental sites and you may be able to find what you're looking for.
Good luck and let me know if you'd like some help.