If you only read Mumbet's comments, you are likely to get a skewed vision of Louisville. He is right that there are times and places that are not as safe as you might like, but I have spent a lot of time in the city, and I've never had a problem. If you are walking in Old Louisville at night, you should be alert, but the odds of you getting mugged are pretty slim. I lived in Old Louisville for about 6 months (at Cardinal Village, which I would recommend if you want to be close to campus and don't mind a kind of generic apartment), and I never had any issues, but I did know people whose cars were broken into. That is something to be aware of. But, all of these problems are limited to Old Louisville. If you live east of campus, you'll be fine.
Also, no one has mentioned living in Clifton/Crescent Hill, which are along Frankfort Ave. Both of those are nice neighborhoods, and usually, you can find some decent prices on rent. Both neighborhoods are starting to get more expensive, but it's still affordable. As someone else mentioned, the Highlands (around Bardstown Road) is a great neighborhood and not far from campus. And, Germantown is an area that is starting to become nicer, particularly if you can find something on the right streets (usually between Eastern Pkwy and Oak St., northeast of Burnett). For all of those areas, you'll have to drive to campus, but you'll be near, if not right in the middle of, the best places to eat, drink, shop, etc. I would avoid living anywhere very far outside of the Watterson Expressway (I-264) because of the commute, unless you have a particular affinity for malls, big box stores and chain restaurants.
Like I said, I have been in Louisville for a long time (almost 9 years), and it's a great city. If you are considering going to U of L, living in Louisville is a bonus, not a drawback.