We went to Grand Tetons and Yellowstone this summer.
For the Tetons, we stayed in Colter Bay, which has been suggested by many others. I thought it was very lovely. You are walking distance to Jackson Lake from the campground. The kids can splash around in the water there, and it's stunningly gorgeous. We canoed on Jenny Lake, which is also spectacular. It's a short drive from the campground.
For Yellowstone, we stayed in West Yellowstone at Grizzly RV, which was very nice. Great place for kids to bike around, and they have a nice playground. There's not much else as far as amenities or recreation, but it's a superb campground. We did have to do a lot of driving to see things in Yellowstone since we camped on the edge of one corner. Some people divide their trip into 2 different campgrounds.
If you take small children to Yellowstone, please be super aware of the safety precautions. Some of the walkways are over very hot springs. Many have railings, but not all do. We were stunned by the number of families letting kids race along these, which was very dangerous. You can enjoy lots of sites without doing big hikes since most of the attractions are fairly short walks from the parking.
I talked about our favorite spots on an episode of the RV Family Travel Atlas podcast, which you can find
here
