Sorry - But - You do understand that Yellowstone is in the Rocky Mountains!
Go to Wiki to see that for the most part YNP is a Mile High with and Average of 8,000 feet soooooo.....
So ..........you will be at your lowest point a Mile High in the park! The good thing is that everything else is pretty high so it is not that big a deal. :)
Not sure if this route is completely free of all perials along the way but IMHO it is extremely Tame -
https://www.bing.com/maps?osid=58fdbbcc-5c87-434a-bc98-68698e1490e0&cp=40.699438~-99.28617&lvl=5&v=2&sV=2&form=S00027
- Look it over to see if it might work - it Comes into Jackson along the River then up through the Tetons to Old Faithful.
Hope this helps,