Just a checklist for the lucky, or wealthy.

I've been to Yellowstone while driving from the east coast to the west, and then Redwod/Sequoia/Yosemite, same trip.
Been to the Grand Canyon because it's 5 hours away, and then hit the Hoover Dam, and used that same trip to get to Carlsbad Caverns... wow.  Then I hit White Sands

That was a week or so on the road, in 1999, when gas was a buck a gallon, and I was driving my 69 Super Bee. 383, 3.23, 727, no AC, but it was April.

https://www.facebook.com/campingroadtrip/photos/a.430431957911/10156173580167912/?type=3&permPage=1

on the other hand, if you're out to see the landmarks, there is a map for that

Here’s the full list of landmarks in order:
 Grand Canyon, AZ Bryce Canyon National Park, UT
Craters of the Moon National Monument, ID Yellowstone National Park, WY
Pikes Peak, CO Carlsbad Caverns National Park, NM The Alamo, TX
The Platt Historic District, OK Toltec Mounds, AR Vicksburg National Military Park, MS
French Quarter, New Orleans, LA USS Alabama, AL Cape Canaveral Air Force Station, FL
 Okefenokee Swamp Park, GA Fort Sumter National Monument, SC Lost World Caverns, WV
 Wright Brothers National Memorial Visitor Center, NC Mount Vernon, VA
 White House, Washington, DC Colonial Annapolis Historic District, MD
 New Castle Historic District, Delaware Cape May Historic District, NJ Liberty Bell, PA
 Statue of Liberty, NY The Mark Twain House & Museum, CT The Breakers, RI
 USS Constitution, MA Acadia National Park, ME Mount Washington Hotel, NH
 Shelburne Farms, VT Fox Theater, Detroit, MI Spring Grove Cemetery, OH
 Mammoth Cave National Park, KY West Baden Springs Hotel, IN Abraham Lincoln’s Home, IL
 Gateway Arch, MO C. W. Parker Carousel Museum, KS Terrace Hill Governor’s Mansion, IA
 Taliesin, WI Fort Snelling, MN Ashfall Fossil Bed, NE Mount Rushmore, SD
 Fort Union Trading Post, ND Glacier National Park, MT Hanford Site, WA
Columbia River Highway, OR San Francisco Cable Cars, CA San Andreas Fault, CA
 Hoover Dam, NV
http://www.randalolson.com/2015/03/08/computing-the-optimal-road-trip-across-the-u-s/