GNP - Not in 2021. MT DOT has road construction scheduled for Highway 2 near the west entrance and Highway 89 near the east side. In addition, GNP has projects scheduled on the Going-to-the-Sun road and also into Many Glacier. This year for the first time GNP is requiring a on-line Entry Ticket Reservation ($2 bucks) ahead of time to even drive through the Park on the Going-to-the-Sun road...
YNP and Grand Teton have no travel restrictions and can handle the traffic, but bear and buffalo jams are inevitable (as tourists you'll be an active participant

). With the new CDC guidelines federal facilities are re-opening visitor centers etc.
Let's pretend for the moment you decide to do YNP/GTNP. When you leave home head west to Sioux Falls and get on I-90 and head west. I'd recommend a stop at Mount Rushmore (If you're staying the night I highly recommend going to the lighting of the sculpture, the NPS will have the timing of the ceremony). Avoid being in the Black Hills during Sturgis... After Mt. Rushmore continue west on I-90, you can do a short side trip to Devil's Tower NM - you can shoot the pet prairie dogs with your camera

.
As you continue west you'll have a decision to make; go over the Big Horns to Cody (you can go over at Buffalo via US 16 or just north of Sheridan via US 14) or do you continue on I-90 into Montana to the Little Bighorn Battlefield National Monument - what I'd recommend. Big Horn mountains are just another mountain, the Battlefield provides a more thought provoking experience as viewed from two different perspectives - a teaching moment. After the battlefield spent the night in either Billings or Red Lodge Montana because...
You're going to take the scenic route to Cody. You'll go to Red Lodge and take the "Beartooth All American Road" over the Beartooth Mountains (US 212)[Charles Kuralt called it "the most beautiful drive in America", I concur]. When you get to Highway 296 (Chief Joseph Highway) turn left, do not continue straight towards YNP/Cooke City. Continue on the Chief Joe and when you get to Dead Indian Pass pull out and read the interpretive signs. This is part of the 1,500 mile route that Chief Joseph and his Nez Perce tribe took trying to out run the cavalry to Canada. His famous quote,
I am tired; my heart is sick and sad. From where the sun now stands I will fight no more forever.
While in Cody the Buffalo Bill Historical Center, maybe the rodeo and on to YNP/GTNP.
YNP things not to miss: If you come in the east entrance via Cody: Yellowstone Lake, Fishing Bridge, after fishing bridge up through the Hayden Valley to Upper/Lower Falls of Yellowstone River & Artist Point. From there you can take the loop back around towards old Faithful and through several geyser basins that have boardwalks to get out and explore. After Old Faithful you can head out the south entrance to Grand Teton NP and Jackson hole.
So when you're done with YNP/GTNP how to head back. No brainer we're talking Lewis & Clark (mandatory reading before the trip; Undaunted Courage by Stephen Ambrose. So where ever you are just head to Threeforks Montana. What an educational, teaching, reflective couple of days this will be. Journey back to 1804, paddling, sailing and dragging a couple boats up the Missouri River trying to get to the Pacific Ocean. At Threeforks is where the Gallatin, Jefferson and Madison Rivers come together to being what we call the Missouri River, named so by Lewis & Clark... When they came to the junction on the way upstream they had to decide which fork to take, as Yogi Berra says when you come to a fork in the road take it... On the way back Lewis & Clark get to Threeforks and decide to split up, Clark says you know I think if I head east over these mountains I'll run into that Yellow River that joins the Missouri, I'll float down it and meet you there at the confluence....
After Threeforks go to Great Falls. There is a fantastic interpretive center of the expedition.
Helena-Lewis and Clark National Forest - Lewis and Clark Interpretive Center
www.fs.usda.gov
From Great Falls go Fort Benton (there was a steamboat the ran from St. Louis to Fort Benton). After Fort Benton Take 80 to 81 to 191 north through the Charlie M Russell National Wildlife Refuge, cross the Missouri. At Malta take highway 2 over to Fort Union and observe the confluence of the Missouri and Yellowstone, pause to reflect on what those men accomplished. From there find your way back home....