Go to Downtown Disney. YOu don't HAVE to shop...wandering around is always fun. Sometimes there's open air entertainment, you can make a computer-generated Mr. Potato Head for free in the Mr. Potato Head store, there's a carousel,
Lego store, etc. Wofgang Puck has a counter service type location that's good for lunch or dinner, and I've heard good things about the Earl of Sandwich. Make it more of an excursion by driving over to Port Orleans and taking the boat to/from DTD.
Go to Disney's Boardwalk. Park at the Boardwalk Inn and walk thru the hotel to the Boardwalk itself. There's street entertainmne(free, one-man-band, mimes, that sort of thing). You can walk around the lake (cool beach, look for duck footprints and tracks), window shop, get your face painted (costs $ but I'd rather do it here where there's some chance of it staying on for the afternoon than at AK, jsut before riding Kali River Rapids!), rent a surry bike.
Resort hop- check out the other resorts in all their Holiday finery. Also check out the "extras" available at the Disney resorts (try disney.go.com) to see what you can do for small fees- like go fishing at POR, or rent a water-mouse. You can always ride the monorail from the CR to Epcot and back- it's usually not very crowded. I think there is also a bunch of fun stuff to do at Fort Wilderness, like petting zoo and pony rides...
If the weather is really nice, drive out to Cocoa Beach and go swimming. Kennedy Space Center might be pricey, but look into the Astronaut Hall of Fame. There is a bunch of cool stuff to see AND do, and I think it's quite a bit cheaper than KSC. You can also drive around the Titusville/Merritt Island/Cocoa area and look for orange groves. Many sell their own juice (free samples!!) and several will let your kids go into the grove and pick an orange or two, right from the tree! We don't get to do this very often in Maine...there are also wonderful birds to spy along the sides of the road, and if there's water in the little canals alongside the road, look carefully at the logs floating- they're gators! We saw alot of these while driving along the highway that runs between Astronaut Hall of Fame and KSC, also some pretty good-sized turtles. I believe Merritt Island has a wildlife sanctuary for hiking/viewing. Often you can stop at the little public parks near the bridges in the Prot Canaveral/Cocoa Beach area and watch for seals and dolphins, and if you're very lucky and in the right area, you might find a manatee or two! No, these are not "sit-in-your-room-and-rest" days, but they are way less stressful and more relaxing than theme park touring!