My little kids and I have started a tradition of going to the zoo on Thanksgiving or on the day after Thanksgiving. Most people don't know that zoos are usually open 365 days of the year. And because they lack the staff to run some of the admission gates in specialty areas, you can sometimes get into them for free. The zoo close to where I am has a lot of newer, inside exhibits and a big dolphin tank so if it sucks outside you can just do the inside stuff.
The best part is there is no jostling with others to get the best view. Little kids always have a hard time seeing what's going on because of all the big folks around. On a holiday, no one is there. Ya know how when big celebrities go shopping and management shuts down the whole store so they can shop undisturbed? It's like that.
A lot of people I know go to the movies on Thanksgiving too. Or go out to eat, trying something you never tried before (but I live in the burbs where a lot of people from different cultures don't celebrate the American holidays - this may not be workable for you - I don't know where you live). But you could just have a movie marathon at home. Jammies, popcorn, candy.
Just some ideas....