Anywhere you're likely to go in Chicago as a tourist is pretty safe. Common sense is required of course, such as don't walk through a dark alley late at night, and there's no reason to do something like that.
I would suggest walking through Millennium Park, then the Art Museum, right next to each other. The architectural tour will give you some history, and it's fun.
As far as food:
- Get a real Chicago hot dog or an Italian beef sandwich for lunch.
- Gene & Georgetti's or Gibsons, as I mentioned earlier.
- Check out the West Loop (restaurant row). Chicago has become famous for having an innovative restaurant scene with diners more open to new experiences. See if you can get in for drinks at The Aviary (it's been a while but you used to be able to email them for a 6 pm reservation). Then try Girl and the Goat or Publican for dinner, which are both about a block away. Or Google any of the other West Loop restaurants. Generally much better options than most of what you'll find in River North and the Loop.