The areas sounding Hyde park, and the south side in general are not all that safe. The areas just north and west are very, very bad. Remember the Chris Rock joke about avoiding any street named MLK? There is MLK Dr running N-S and on the western border of Hyde Park, just west of U Chicago. Chicago has one of the highest crime rates of any major city. Just make sure to use common sense precautions, don’t walk alone and be especially careful after dark. I worked and traveled in the area for years, and the major safety concerns for a student are going back and forth from the loop after dark. Buses and the el are fine, I’ve never had any issues at any time of the day or night.
The lake front trail is a great place to jog or ride your bike.
I’d only be concerned about racism if you are a black conservative. Chicago is a rough and tumble Democratic union town, full of good people and corrupt politicians. Most people will just see you as a college student.