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.