From their description I'm guessing Northeast Minneapolis. It is an old blue-collar area currently being revived, and has quite a few older 3-story houses.
A lot of the old warehouse buildings have been gutted and renovated, turned into office spaces, breweries, lofts, restaurants, and coffee shops. Its also considered the arts district of Minneapolis.
I think the crime used to be worse than it currently is, but I'm not certain of that. I started working in the area a few years ago, and I haven't witnessed anything unpleasant. It feels quite safe here.
If you go across the river to North Minneapolis, you'll run into a rougher neighborhood with bars on windows and stuff like that. But even then I've heard things are improving over there too.
The Central neighborhood, just south of Lake St. It's not as ...hmm... exciting as North, granted, but I can still point out the leader of the local gang if I see him and his compatriots driving around.