Midway is crawling with cops, so no worries at the actual airport. The immediate area isn't particularly rough, although it's not too far from some rough areas; in fact, one thing about Chicago is that the 'bad' areas aren't really clearly delineated anymore. You can walk two blocks and go from solid middle-class to really challenged neighborhoods.
Downtown is big enough to have different areas within it; the West Loop (the densest business district) is well-patrolled and extremely populous during the day (say, 7A - 6P or so), but gets surprisingly empty after typical office hours. Traditionally, this area is relatively safe.
River North (where lots of the hotels are) is similar, although there are more residences and, therefore, more after-hour traffic. It's also got more night-life, which of course draws in more crime.
I'm not aware of any OC restrictions, but knives are theoretically limited to 2 1/2" blades within the city; that said, I've never known a person (not being arrested for something else, that is) who was even spoken to about a knife by a Chicago cop. Stun guns are, IIRC, the same as a gun.
Chicago has become a violent place, and the violence isn't quite as contained to the 'bad' areas as it used to be. We've seen violence on Michigan avenue in the past few years, something not common previously, and some crime in the loop has been increasing also. Essentially, encourage your wife to stay in groups, avoid walking where possible and not consider anywhere in the city really 'safe'; the bad guys have discovered cars, apparently.
Larry