Don't fly anywhere.....unless you like maschochism. Not during Thanksgiving weekend, unless you have to.
I'm guessing that, if you want to get out of Chi-town, you already know the city. It's a great town, some nice sites, great food, etc.
Instead of buying a ticket, rent a car. Whether you head south/west thru Springfield (some Yankee history) and over to St Louis.....or you head north/east along the lake or up thru Wisconsin/Upper Peninsula of Michigan, there is a lot to see and do around those areas.