I lived in Over the Rhine for several years during college, single female/living alone/no car. I liked it, but none of my friends and family would come visit me down there I lived in what I call "shallow OTR", just a few blocks from where the city and the ghetto meet, and it wasn't too bad, but I tried not to venture too often into "deep OTR". My school was just a few blocks away, and for the most part I felt comfortable walking back and forth at all hours (although that may not have been wise).
I was there I guess two years? During that time, I witnessed a bit of violent crime (my neighbor was robbed at gunpoint; there was a shooting outside the school) but didn't personally experience anything. My bike was stolen (still sad about that) and I was harassed once when I went walking through deep OTR. I'm not saying any of this to scare you, just to give an honest picture. If I could move back into my old apartment I would in a heartbeat. It's been a few years since I lived there, but in those days there were a lot of festivals and art walks happening on Main Street. The architecture is very nice as well.
As far as living without a car -- doable, but it might help to make friends with someone who does have one. There's not a lot in the way of groceries in that area. Findlay Market is great for produce and meats and cheeses and such, but not so much everyday shopping. There is (or at least was) a Kroger over on Vine, but it always seemed pretty sketchy to me so I'd usually get someone else to drive me over the river to the Kroger in Kentucky. (Kentucky is actually very close-- walkable, really.) As far as getting to UC, I took the bus there a few times without a problem, though I can't say what a day-to-day commute would feel like.