Yellowstone is mostly visited by locals, with relatively few visitors from other areas. Overall, it's a very pleasant attraction, perfect for children. You can admire the wonders of nature, and most of the time you're walking in the center of the Earth, which is cool and not too sunny. Plus, there's plenty of water to play in, which is sure to be fun for the kids.
Unfortunately, some uncivilized tourists littered and carved their names in some areas, which was really heartbreaking.
Overall, it's a worthwhile attraction. The center of the Earth lasts a little over an hour, but if you want to spend more time exploring the surface, the scenery is also very pleasant.