I happily live in the "murder & drunks" neighborhood shown on the map above. My neighbors are either senior citizens or young couples with children under 5. Whenever it snows in winter, every part of the sidewalk on our street is completely shoveled down to the cement within eight hours, and the alleys are always plowed by people who live in the neighborhood way before the city even thinks about taking its plows to the alleys. One of the worst things I have to contend with is the guy from a couple blocks over who walks his dog on our street and doesn't pick up the dog's crap. There are two schools within five blocks of my house -- one was built a year ago and the other was completely remodeled at that time. People here sit on their front porches in the evening and are friendly to those who walk past. The houses are old, but generally very well-maintained, and most of them have gardens of some sort.

I realize that none of this is specifically what you asked about, but I think it shows that sometimes reputations are not entirely accurate. There are no bad parts of Duluth, despite what some people may tell you. There are places, however, that have a lot of turnover; I'd avoid those blocks.

I would just make sure the actual block you are moving onto isn't too run-down, but even that can be deceptive, since you might find a really stellar apartment in the hillside with a great view for very little money.

All of that said, you probably want to live in either the East Hillside or Chester Park, because that's where your chances are best at 1) finding a rental apartment as opposed to a single-family home, 2) being close to the places you want to frequent, and 3) finding other people in their 20s with similar interests.