One of the best places to go in Branson at Christmas is Silver Dollar City. For people who don't ride rides, it's still a beautiful place to walk around under the Christmas lights and grab a hot chocolate or skillet meal. You can see pictures
HEREThe weather can range from very cold that time of year with winter precip or pretty mild, so you definitely have to pay attention.
We really like the Tall Pines campground, but I wouldn't say the roads are especially level. Branson Landing isn't a very scenic campground in the park, but it is on the edge of a lake where you can do some trout fishing and has a very flat campground with easy access to the roads.
I think you can find plenty to do to keep busy if you like seeing shows and have the money to put into them. Walking around the lakes or the Bass Pro Shop offer a good place to spend a couple of hours for free. The Ralph Foster Museum at the College of the Ozarks is interesting, too.