My list from my memories as a kid. I was lucky that even though we had limited funds, my parents bought a Sears tent and sleeping bags and we car camped all over the west.
1. Yellowstone. While we saw lots of geysers, I specifically remember watching Riverside Geyser erupt. We also saw lots of bears, including some in the campground several nights we were there. That doesn't happen much anymore. Anyway, Yellowstone was the worlds first National Park for a reason. With geysers, a spectacular canyon with amazing waterfalls, wildflowers, and pristine lakes including Fishing Bridge where one can look down at great numbers of cutthroat trout, Yellowstone has a bit of everything. While you're in the area, Grand Teton is also great for kids. I remember taking the boat across the lake and hiking up closer to the Tetons. Wildlife abounds here, too.
2. Mesa Verde NP. I remember climbing around the ruins and looking at the displays in the museum. Even at that young age, it gave me an appreciation of other peoples and how their customs and history was different from mine. While in the area, take the Durango to Silverton Narrow Gauge Railroad. I remember my first trip aboard that train. A real steam engine! And Silverton was and still is a real honest to goodness western mining town with wooden sidewalks. A little more touristy now, but still a memorable trip for kids and adults alike.
3. Arches NP. Since I first camped here in the late 60's, I've been back many, many times. Devil's Garden CG is one of the two most kid-friendly CG's in the NPS system. If one can do w/o hookups, one can park and play for several days without ever getting back in the car. Rocks to play on, arches to climb through, sand dunes to slide on, and deer in the CG make this one fun CG. And I like the canyon views from the nearby Island in the Sky part of Canyonlands NP better than those of the Grand Canyon.
4. Zion NP. I first hiked the Zion Narrows in Boy Scouts in the 60's when we didn't encounter anyone until the last couple of miles. Now, it's a favorite for many and still a great hike (just watch the weather to avoid rain). So many other great hikes in the canyon make this a fun place to explore. Camp at Watchman CG in the park. Some electric hookups. But the real catch is the Virgin "River" which flows beside the CG. Kids (and adults too) build little dams in this usually slow flowing stream and splash, wade, or sit in the water to cool off under the Cottonwood trees. For kids, this is one of those CG's that is as memorable as the rest of the park.
5. Since you just said Out West National Parks, I'm going to throw a curve at you and recommend Banff, Jasper, Yoho, and Kootenay NPs grouped together on the border of Alberta and British Columbia in Canada. Absolutely no family camping trip of my youth stands out in my mind as much as our trip to those parks. My little photo album from that trip is filled with many waterfall pictures, but there are also some of Lake Louise, Moraine Lake (even prettier than Lake Louise IMHO), the Columbia Icefield (although it has receded a bit), and wild animals galore. Glacier is pretty, but it's only a taste of what the Canadian parks have to offer. I've been back a couple of times since, and I'm itching to go again. Words can't express how gorgeous these parks are. Plan on three weeks if possible. It's a long ways, so make the most of the drive.
Ken & Allison
2 Camping Cats (1 diabetic)
1996 4Runner, TRD Supercharger, Edelbrock headers
2007 Fleetwood Arcadia, Honda EU2000i
4 mountain bikes, 1 canoe, 4 tents, 8 sleeping bags, 2 backpacks
(You get the idea!)