Your question got me to researching something I'd been think about:
We've been to 72 NPS locations - not all of which have campgrounds.
National Parks - 23
Glacier Bay - on a cruise ship
Hot Springs
Petrified Forest
Grand Canyon
Pinnacles
Kings Canyon
Yosemite
Redwood
Mesa Verde
Glacier
Great Basin
Carlsbad Caverns
Crater Lake
Badlands
Big Bend - spent 4 months there as a campground host volunteer
Arches
Capitol Reef
Canyonlands
Zion
Mount Rainier
Olympic
North Cascades
Yellowstone
plus
20 National Monuments
1 National Preserve
8 National Historical Parks
3 National Historic Sites
6 National Memorials
5 National Recreation Areas
3 National Seashores
2 National River/ Wild and Scenic Rivers
1 National Parkway - driven full length