Some of the stores will have "specials" on Friday from 6 a.m. until 8 a.m. so some such time. Some specials will last until noon! However, many of the sales will continue at least through the week end if not for the entire week....and then there will be "new specials"!
The Museum of Science and Industry is open on Thanksgiving Day. In the past the store windows were decorated for Christmas by Thanksgiving. I always enjoyed going to a museum and then looking at the store window decorations that day. There were people dressed in jeans and sweatshirts (and perhaps a parka depending on the weather) and others in spike heels and furs coming from some elegant restaurant.
I am sure you will find a number of restaurants open....many serving the traditional American Thanksgiving turkey dinner. You will also find many TVs on and tuned to a football game!
Enjoy Chicago over the holiday!