What is the best NP camping experience?

My vote is for Glacier then Tetons back when we were young and strong enough to do some hiking.

Each National Park is unique preserving and interpreting vegetation, wildlife, scenic, recreation, history, archaeology, and culture. There are 417 units in the National Park Service, and many have camping. That is a lot of varied interests and parks. What is "best" really depends on what your interests are.

"Dry camping is OK, as long as I can run my small generator once or twice to recharge the battery."

Why limit your dry camping to places where your generator is allowed?

Try Gros Ventre in Grand Teton NP. Just North of Jackson Hole. Dry camping only, but the campground fills up later than the popular campgrounds that have power. Near the river, often see moose within the park. We have never needed reservations there.

These all can be booked online and dry CGs usually allow generator hours:

Fishing Bridge in Yellowstone has full hookups. We saw Elk in the campground, and a bison wandered through our loop one afternoon. Good location.

Colter Bay RV Park at Grand Teton NP has water and electric.

Grand Canyon's Trailer Village CG (south rim) has full hookups. Lots of Elk every day. The park shuttle stops at the CG entrance. The North Rim campground has dry camping, water available.

Zion Watchman CG as noted above has electric, and is a short stroll to the shuttles and Visitor Center. Some sites right on the river.

Rocky Mountain NP Has dry camping with nice views at Moraine Lake, regularly visited by black bears. Shuttle about a 15-minute walk.

Bryce Canyon has dry camping, shuttle stop nearby. Acadia NP, same.

Devils Garden CG in Arches NP is currently closed for road work, but has dry camping amid great red rock scenery.

Everglades NP has electric hookups, a short drive to marina and visitor center where crocs and gators coexist in same waters, highly unusual.

Lots more out there, but those come to mind from past visits.

Camped in
Yellowstone
Tetons
Grand Canyon
Big Bend

They were all great experiences

The one we enjoyed staying in the park was Zion NP. It has 30 amp power and water, but no sewer.

In the summer season, I vastly would prefer to be in the park, within walking distance of the shuttles, to avoid the long entrance station lines.

We also enjoyed staying in Big Bend NP. This is mainly a winter season park for a rig as large as yours. Rio Grande Village CG is dry camping, though there is a small parking lot type FHU RV campground run by a concessionaire. Big Bend is large, you could easily be driving almost 200 miles round trip from the closest off park FHU campground to see the sights.

Another that we have not been to but would consider staying the park essential is Death Valley. Another winter season park. There are some FHU sites available at DV, and lots of dry camping.

Closer to northeast Florida - I'd want to stay in the park at Great Smoky Mountains NP, and Mammoth Cave NP for a few days.

It is not a national park, but the USFS campground at Ocean Pond near Lake City is a nice campground which offers a very rustic/rural setting.

I have to lump Yellowstone and the Tetons together. One without the other is almost a wasted trip.

Grand Tetons