Rochester can be a tough place to live if you don't know anyone- I moved here when I graduated from HS in 2008 and really struggled the first couple years, until I got started in my nursing program
and met some really good friends (you already know how going through nursing school brings you together).
My advice is to move in with someone similar in age/interests to you (same gender too). If you have a family member here, don't move in with them, it will discourage 'branching out'. (I moved in w/ my sister, free rent was nice, but hard to make friends).
As creepy as it sounds, search craigslist for places to live if your having trouble finding someone. You'd be surprised by how many young nurses and health care professionals are looking for a roommate, and if they work at mayo, they are probably not a creep and can obviously pass a background check (always a positive)
Be outgoing! going out for dinner and drinks is fun here because there is a nice downtown area.
If possible, try to live as close to mayo/downtown as you can- it makes it a lot harder to get together with people when you live on 'the north side' or in my case 'the south side' as was my case.
I've been in your shoes! if you have any questions, just ask, i'd be happy to help!