MeddlingKid
Perhaps I will try to stay downtown then. I am just a bit concerned as to whether I can get from my interview (which is supposed to end at 12:15pm) to the hotel to grab my bag to Midway for a 2:40pm flight. As for crime, I've been working on a project in downtown Detroit for six months, so it'd be something I'm used to.
In general I recommend people stay downtown because you get a much better feel of Chicago, and theres a lot more todo at night, but if you are coming in late, leaving early and doing absolutely nothing other than checkin in, sleeping, interviewing and checking out, it really doesn't matter where the heck you end up staying.
Also, crime really isnt an issue in Hyde park... honestly.
As for your plan.....Its a bit tight -- depends on your risk aversion i guess. I'd suggest you just bring the bag with you to the interview, its no big deal - a lot of people do. HP to downtown is approx 15 to 20 minutes by car, assuming you finish at 12:15 on the dot, get into your cab by 12:20, youd be at your hotel by 12:35 or 12:40 - ten to fifteen minutes to get upstairs, grab your bag, check out, back out by 12:55pm, back in the cab to midway by 1:00, you should be there by 1:30pm to 1:45pm - giving you approx an hour to make your flight.
edit: If your flight is out of ohare and not midway (which I thought it was) this would be quite tight. Traffic on fridays is hard to predict, it can take 20 minutes to get to ohare from downtown, or it can take 45 minutes to an hour.