Best advice I can give is to get into the park early. By early, I mean you should be in past Mammoth by 445. Daybreak is the best time to be there anyway. And you won't have any company other than the sights and wildlife.
Get over past Mammoth and head east.Spend your morning in the Lamar, then head out of the park over Beartooth and make a day trip of that. Maybe incorporate Dead Indian Pass intoitand return via Cody. Or drive up through Red Lodge and then to the interstate, over to Livingston and back down to Gardiner.
Another day, same thing but head south of Mammoth early. Just hit what you can and what interests you and the exit the park late morning-midday. And go elsewhere.
That time of year, that is the best you can do. Be there before sunrise. You will see more and deal with way fewer tourons.
Going out the east entrance used to be a good drive for wildlife. Not sure how that stacks up anymore. Cody is ok, but big-time touristy.
