I wasn't a huge fan of Yellowstone. Granted, I would do it differently if I did it again. The car camping was super over crowded, which I guess is to be expected. The Black Hills was way more up our alley, but again, I'm sure everyone's experiences differ.
My best friend was a seasonal ranger in Yellowstone for a couple of years, and he had similar complaints about the crowds and mess in the high-traffic areas...the trick to any of these big parks is to find the off-the-beaten-trail areas. Talk to rangers -- see if they can recommend something a little more adventurous, or an area that is not as popular with tourists because of difficulty, distance, etc.
If I went again without kiddos I would def do that. Even some more backcountry stuff and/or flyfishing. Gah, sounds heavenly.
Yellowstone is amazing in the winter. You can ski and snowshoe in and there are no crowds and it is quiet and beautiful. Also, in spring you can ride in before they open the roads to traffic.
Yellowstone can be super great in the summer too. It is just important to get backcountry camping permits. There are many multiday backpacking trips where you can stay at hotsprings each night. Once you are a mile from a trailhead, you won't see anyone else. Not that it solves travelling through the park and getting stuck in bison jams.
I love going to the bigger parks in the off season. Winter in Yosemite was probably my favorite. You have less crowds and get to see the parks in a completely different light. The downside is sometimes areas are closed or inaccessible.
what I recommend to new backpackers is to learn as much as you can and get to the point where you can safely and comfortably hike in shoulder seasons and of course during the winter!
This is a wonderful way to hit the national parks and wilderness areas we are blessed to have in the U.S.
REI member since 1979