i live in WestTown near Humboldt Park and love it. The Humboldt Park (east side of) is up and coming. There are a lot of more affluent young professionals moving into my neighborhood because of the potential for home value increase and the proximity it is to the beautiful park. I have a wife and daughter and feel very safe around here. the neighbors are great and the alderman in Humboldt is a strong one who looks to improve the neighborhood and community. I say go for it! it would be a wise investment.
I wouldn't worry about the "up and coming" areas in this market. I'd be more interested in finding an established neighborhood that has stood the test of time. Like a Lincoln Park, Lakeview, Old Town, Bucktown, Wicker Park or West Town. West Town is a big area and there are some parts of it I would stear you away from. The place on Warren is questionable. I think in and around the place you mentioned on Grand is a better bet.
Again, click on link below and see if that helps. Like I said, I live over there and love it. Good Luck!!