My wife and I took our kids (now 13 and 15) to Yellowstone for the first time. We had been for our honeymoon in 2001, but this was before kids and long before I fly fished. Such a beautiful place, and it goes far beyond just the unique geological stuff... the Lamar and Hayden Valleys are amazing places to view wildlife. In fact we were lucky to witness a griz feeding on a bison carcass from a nice healthy distance away across the Yellowstone River (the vehicles across from us in the 4th picture down are all there to see the griz). While the brunt of time was spent touring around, my son and I did manage to wet our lines a couple of times in the Yellowstone and Soda Butte Creek.
I most definitely plan to go back. Lots of walk and wade opportunities in the park, and amazing looking floats on the Madison which I may try to do next time. The folks at Blue Ribbon Flies were super helpful, friendly, and very knowledgeable (and will steer you in the right direction).