There are several shuttles to various areas in Baltimore. The area within walking distance of the hospital is not safe.
My first suggestion is to sublet an apartment in Charles Village. There is a shuttle stop on the corner of 33rd St and St. Paul St (mapquest it). This is where the university campus is. If you live within walking distance of that shuttle, that is a safe area with some nice places to eat/drink. If you go to
www.jhu.edu and search for "JHU Shuttle" or "JHMI shuttle", you can see the routes.
There is also a shuttle from Patterson Park, but I'm not sure of the route. While it is a more popular area, it's not as safe.
You can definitely find a cheap place to live in Charles Village. Search for sublets on craigslist or the JHU Gazette. I live in Hampden (neighborhood just west of Charles Village, and I work on the Homewood (university) campus. Best of luck in your search.