Hmm, this may take a little while.
First, in my Passport books:
Jean Lafitte National Historical Park & Preserve New Orleans, LA
Jefferson National Expansion Memorial St. Louis, MO
Ulysses S. Grant National Historic Site St. Louis, MO
Lewis & Clark National Historic Trail St. Louis, MO
Mammoth Cave National Park Mammoth Cave, KY
Vicksburg National Military Park Vicksburg, MS
Castle Clinton National Monument NY, NY
Statue of Liberty National Monument NY, NJ
Dayton Aviation Heritage Natl Hist Park: Cycle Shop Dayton, OH
Effigy Mounds National Monument Harpers Ferry, IA
Rocky Mountain National Park Estes Park, CO
Dinosaur National Monument Jensen, UT
Hagerman Fossil Beds National Monument Hagerman, ID
Florissant Fossil Beds National Monument Florissant, CO
Minidoka National Historic Site Jerome County, ID
Craters of the Moon Natl Mon & Preserve ID
Oregon National Historic Trail ID, WY
Yellowstone National Park WY
Little Bighorn Battlefield National Monument Crow Agency, MT
Theodore Roosevelt National Park, South Unit Medora, ND
Wind Cave National Park Hot Springs, SD
Badlands National Park Interior, SD
Minuteman Missile NHS Wall, SD
Haleakala National Park, both sections Maui, HI
Independence National Historical Park Philadelphia, PA
Gettysburg National Military Park Gettysburg, PH
California National Historic Trail WY, UT
John D. Rockefeller, Jr. Memorial Parkway WY
Natchez Trace Parkway MS
Blue Ridge Parkway VA
Grand Teton National Park WY
Santa Monica Mountains NRA Santa Monica, CA
Juan Bautista de Anza National Historic Trail CA
Sequoia National Park Visalia, CA
Fossil Butte National Monument Kemmerer, WY
Well, that is all the stamps in my passports. But I have been to a few other places, will have to check by memory now.
Flaming Gorge National Recreation Area WY, UT
Everglades National Park FL
Shenandoah National Park VA
Boston National Historical Park Boston, MA
Mount Rushmore National Memorial Keystone, SD
Arlington House, The Robert E. Lee Memorial Arlington, VA
United States Marine Corps War Memorial Arlington, VA
Lincoln Memorial Washington, DC
Thomas Jefferson Memorial Washington, DC
Washington Monument Washington, DC
Vietnam Veterans Memorial Washington, DC
Arlington National Cemetery Arlington, VA
Appalachian National Scenic Trail VA
I really like our National Park system. Wish I had some skill sets for getting hired there. The Parkways and Trails I have spent some time on, either driving or hiking. I have driven through some other NRAs, but only included the 2 I spent any time in looking around. And I guess Flaming Gorge does not count, since it is actually part of the Forest Service.
I need to get back to DC sometime. Haven’t seen the Korean or WW II memorials yet. But there are a lot of other places I want to get to also. I have a lot of room in my National Park Passport yet. 
We are doing other countries too? Not too many yet. None at all in Dominican Republic, Italy, and India.
Canada, several Provincial Parks, but for national:
Georgian Bay Islands National Park Ontario
Australia, confusing set up, a lot of stuff is called National parks, but ran by the states and/or territories:
Uluru-Kata Tjuta
West Macdonnell
Watarrka National Park
Port Arthur
Richmond Gaol
UK:
Peak District