I lived in Hyde Park for twelve years (1987 - 1999), so what I know is mostly history now. I loved living there. There was some crime, but not more than you would have to deal with in any urban neighborhood.
It was a diverse community, with easy access to public transportation, a direct line downtown on the Metra, and great access to the lake. I thought there was a strong sense of community, and it was easy to get plugged into a social network.
Much of what goes on in HP revolved around the U of C---I was a student and then a staff member there---I don't know what life would be like for someone with no connection to the university.
I had friends who lived in South Kenwood, which was more residential and a bit quieter. Mostly they rented rooms in the big mansions (or served as house sitters).
Back in the 90s, no one I knew lived in Woodlawn because of the crime, but I have heard that things have changed in the past ten years or so. E 63rd street used be blighted, but I believe it's better now.