Some of the less visited national parks and monuments are wonderful, plus there are some great state parks. I recommend:
Black Canyon of the Gunnison National Park
Great Sand Dunes National Park
Colorado National Monument
Theodore Roosevelt National Park
White Sands National Park
Gulf Islands National Seashore (visit in early spring and fall)
Pictured Rock National Lakeshore
Voyageurs National Park
Grand Portage National Monument
Cape Hatteras National Seashore (visit in the fall)
Mt. St. Helens National Volcanic Monument
Badlands National Park (visit after Labor Day)
Wind Cave National Park
Big Bend National Park and Big Bend State Park
Bandelier National Monument
Canyon de Chelly
Devils Tower National Monument
Jewel Cave National Monument
Little Bighorn National Battlefield
Mojave Trails National Monument
Rio Grande del Norte National Monument
Saguaro Forest National Park
Everglades National Park
Blue Ridge Parkway
Natchez Trace
Some wonderful state parks include:
Palo Duro Canyon (Texas)
Cloudland Canyon (Georgia)
Custer State Park (South Dakota) visit after Labor Day.
Topsail Hill Preserve and nearby Grayton Beach (Florida)
Silver Springs (Florida)
Pipestem State Park (West Virginia)
Fort Abraham Lincoln State Park (North Dakota)
Itasca State Park (Minnesota)
Chimney Rock (North Carolina)
Tahquemenon State Park (Michigan)
Davis Mountains State Park (Texas)
Black Mesa State Park (Oklahoma)
I’ve found September and October are the best months to visit many of the extremely popular national and state parks. Children back in school plus cooler weather reduce the crowds and make reservations easier to snag.
It has been 15 years since I’ve been to Yellowstone and nearly 20 since visiting Yosemite. I understand both have huge crowds except during the middle of the winter.

Wyalusing State Park Wisconsin.
My favorite is still DEAD HORSE POINT Utah. First there in 1955. No paved roads, no walkways, no guard rails, no drinking water, rock cairns everywhere from people making Uranium claims.
Now the roads are paved, walkways everywhere service entrances guard rails. Still magnificent!