Beth Israel is in the heart of college student land. The rents tend not to be cheap, although they are coming down. I lived in a very nice building at 12 Stoneholm Street. At the time, a one bedroom went for 1100. I heard it is much higher now. Maybe around 1600. The building has a rooftop pool, parking garage (extra cost) a sauna, excercise room and is in the middle of everything.
Around here you have to pay fees to agents to get an apartment, which can run a full months rent on top of first, last and a one month deposit -- so be careful. Other nearby or easy transport places to live are cambridge, brookline, brighton, newton. Neighborhoods in boston proper -- Back Bay, South End, Beacon Hill. Mission Hill and Jamaica PLain are near BI, but not so safe. Go to www.craigslist.org
and click on the boston edition to look at ads. Remember the DNC is coming in July, so some people have rents jacked for that, or don't want to rent until that is over. Good luck!!!
As far as schools go, are you looking for a nursing grad school or for your kids? Grad schools in the area include Northeastern, Boston College, Simmons, Mass General, U Massachusetts and Regis. If it is school for your kids, look at Brookline and Newton.