A bunch of good stuff already mentioned ITT earlier, but a few comments from my trip with elementary school aged kids.
Pretty much all of the towns in yellowstone have a good ice cream shop. Each new town that we went to, we tried out the ice cream, and it was a lot of fun for the kids.
If you're into fishing, then fishing yellowstone lake is pretty cool. Our family went out on a 4 hour fishing charter trying to catch lake trout and cutthroat trout. Just trolling, so if the kids are patient, it can be fun. We caught probably 4-5 good sized trout on our charter.
Lamar valley is always cool, as you'll get to see tons of game. Bison likely on the road, or right near it, antelope, etc. This was a picture I got of one shedding.
The yellowstone falls (grand canyon of yellowstone) was awesome. It's a lot of steps up and down to get to the different observation points, but if you're up for it, it's amazing.
Old faithful is cool for a little while, but after a couple hours, it got a little old for the kids. Also, it is typically super busy. The mammoth hot springs up north was a lot less crowded. Not as cool of eruptions as old faithful, but it's a nice walk around some of the springs.