Most of downtown is quite safe.  If you plan to venture out at night, stick to River North (north of Wacker Dr., along State and Michigan), with all the late-night venues.  Don't stay in the Loop area; it's bustling during the day, but pretty much turns into a ghost town when the office workers go home.  I walked it at night, and was OK, but not comfortable, either.  Hotels are equally nice in both neighborhoods, although the Loop has really good lunch places.

If you don't like downtown, stay in Rosemont, Schaumburg, or Oakbrook.  They all have lots of nice hotels, restaurants, and entertainment options in the area.