I;ve lived in Rochester all my life. Yes, bring your car. Where are you from? If you are from somewhere warm, you will be learning how to drive in the snow!
I think the U of R uses Strong and Highland hospitals. Near each other but definitely NOT walking distance.
There are houses for rent to students all around the hospital but you will have to look because I don't know how often one actually opens up. There are many apartment buildings and houses to rent in and around Rochester. There are some REAL nice houses that are divided up into apartments in the Monroe Ave/Park Ave/East Ave areas and neighborhoods. Not totally close to the U of R but nice.
I would call U of R student services and find out and maybe have them send you some local classifieds. Or search online too.
The School of Nursing is really great. Helenwood Hall is pretty. I worked for them as the medical assistant for one of the high school clinics that the CNC sponsored.
Here is a link to our newspaper: http://www.rochesterdandc.com/apps/pbcs.dll/frontpage
Maybe you can start with the classifieds there.
or try: http://www.inforochester.com/newspap.htm
Good luck and welcome to Raa-chaa-chaa!
EDIT: Watch what area you move too, Genesee street, West Ave, Plymouth Ave, and the parts of Mount Hope towards the city...maybe stay away from. South ave area is nice, near Highland Hospital where you'l probably do clinicals. There are more nice places than not-so-nice but you just want to know what you are getting before you sign the lease!