I will be posting some weekend events (if you're not too busy shopping), but one of my family's favorite things to do on Thanksgiving weekend is go to a holiday light display. Most of the major light displays are getting started (if not this weekend, for sure next weekend), and now is the perfect time to check them out before the season gets too busy.
My favorite public displays include Garvan Gardens, Pine Bluff's Enchanted Lands of Lights and Legends and Burns Park's Funland drive display. More information can be found about each of these displays and a few more. I have some information on good neighborhoods to drive through, but most residential areas don't get really going until later in December.
It's also a great time to check out the ice skating rink at the River Market. More info.