These old post may have some information useful to your Quest:
Route 66 Plus :C Route 66 NM & AZ.
As someone has mentioned, most of Route 66 is now covered by I-40, in places there are sections of it still, usually labeled as Route 66. At least I have seen it in NM, AZ & CA as well as OK.
My wife's mom used to live right off Route 66 in La Verne (called also Foothill Blvd.) in CA. My wife's family used to drive Route 66 to get to Pennsylvania when it was the route to take.
One would almost have to cross the Route in going to Yellowstone, etc. & could also pick it back up by heading South out of Montana.
Ooophs! Sorry about the Double Post, Not sure what I did?????