I currently go to the UR and I have lived on campus, as well as on the road with Strong Memorial Hospital, but down a ways. I love living on campus because of the convenience of being so close to the hospital (where I worked and volunteered) and by the buildings I have class in as well.
Given that a friend told me we will primarily be at Strong and the School of Nursing building (on Crittenden - the road right behind the hospital), it seems logical that living in the White Coat Ghetto (that primary area) would be best/easiest.
I used that same website and put a deposit down on one of the rooms in a house on Crittenden beginning in May. The house is literally across the street from Strong and a block up the street from the SON building.
One of the worst things in the winter in Rochester is the ridiculous amounts snow and it is SO, SO, SO nice to not have to worry about dealing with it everyday. If you can avoid the hassles of digging out your car, possibly bad driving conditions (especially if you need to be up earlier than the snow plowers), and then having to be bused from a parking lot for students miles away -- just to get to class or clinical (!!) -- it is worth it. Even if it is more expensive, you will be much less stressed and get a lot more sleep - and from what it seems, we all are going to need as much of that as we can get!
As for living on the other side of the river - the 19th Ward...it isn't a terrible option if you're looking to save money. I know a lot of people who lived there over the summer and during the school year and for the most part, they didn't mind. The area isn't known for being the best - there are occasionally break-ins, robberies, and jumpings. I don't suggest walking around by yourself in the evenings/late at night or very early in the morning just because people have been known to be robbed in these cases, so keep that in mind.
On the flip side, the people in the neighborhood are usually very friendly and there is a decent amount of students who live there. I stayed at a boyfriends house on most weekends last year and in the mornings a lot of people go for a walk or sit outside and read the paper. Most people would say good morning and ask how you're doing, which was really nice and I felt totally comfortable walking by myself during the day.
Housing is relatively cheap compared to the White Coat Ghetto, but often you need to rent the whole house and work out finding roommates/everyone paying rent on your own. The walk to the med center/SON is about 10-15 minutes, and there's even a bus that runs on weekdays from the morning until late into the evening. It goes to River Campus, and then its a short walk to the med center, so it's pretty easy.
Let me know if you have any other questions!