I didn't say this before, but I highly encourage reservations at the "go to" campgrounds for each park. We did that our first year, and it completes the "national park experience".
I mean, come on, spending the night in the back of Arches, watching the sun set on the park and then climbing down off the rocks and into your camper....how cool is that? VERY COOL! Would have been a different trip to have to drive 45 minutes back to a pack and stack campsite in Moab.
Camping at the Watchman in Zion right on the Virgin River and surrounded by the majesty of Zion! Again...much better than driving out of the park each day.
Watching the animals in Hayden Valley of Yellowstone until well after dark, knowing that in 15-20 minutes you'll be in your camper.
Watching a storm move in over snow covered peaks in Grand Tetons while your camper is being surrounded by moose. Sure, you could be in Jackson Hole closer to a restaurant, but I don't do National Park trips for the food.
I could go on and on. There are cons to it sometimes. Like no electric and water in Arches. It was a challenge, but sooo worth it!
Figure out the premier option each park has for camping within the experience. It will feel more like camping, and that's not a bad thing! :)