You could always camp somewhere beautiful if you want or do outdoor stuff. Chicago is awesome during the holidays for ice skating and museums. The Natural History Museum might be a good idea.
Springfield, IL is a wonderful, there is the state capitol, and the Lincoln Museum which is exceptionally good. You can also take a side trip to New Salem.
Taking them to Chicago is always a great option. There you've got sports, food, tourist-y sites, music, and an overabundance of activities aimed at families. It's a fun town.
