I live a couple hours from Branson and we spent a long weekend there last year. We stayed at
Jellystone Branson Which was an awesome park for the kids, but it's actually in Forsyth, MO not Branson. I would say probably 15 minute drive from Branson. Which isn't a bad thing if you are looking to have a place for the kids to have fun when you are not on the strip and you want to avoid the traffic.
I have heard very good things about
Wilderness Campground at Silver Dollar City. They have a free shuttle to Silver Dollar City and the water parks. Again avoiding the traffic of Branson. I also hear that they cater to kids as well. When my kids are older and wanting to enjoy the theme parks, i will probably start camping there.
Hope this helps. Enjoy, it's beautiful there.
Spap