is easy! But Cody
TO Yellowstone, I think that's the question
The grade and altitude of US 14/16 into the East Entrance is fairly gentle-- roughly comparable to Donner pass, which we did with our "heavy" 2619 yesterday. But because it's more twisty, you won't be able to sustain 60 MPH, and so you'll be in 3rd most of the time.
No problem. You know that Teddy Roosevelt, a man who traveled through A LOT of places, called that road the most beautiful in the world? But I think he missed by 20 miles-- he never had a chance to travel the NE entrance US-212 route. But with an extremely steep grade up from Red Lodge, and topping out at almost 11,000, you and I would be spending a lot of time puffing hard in 2nd (at best).
If you arrange to leave by way of Mammoth, you could return to Cody via 212 and 296 "Chief Joseph's Highway" instead of taking the same road out.