Things on Route 66 that come to mind:
Holbrook, AZ - the Wigwam Motel
Winslow, AZ - Standing On The Corner
Seligman, AZ
Oatman, AZ
Amboy, CA
Radiator Springs in the movie was modeled after a composite of locations, but it's said the main inspiration was Peach Springs, AZ on 66 between Seligman and Kingman. That stretch is the longest remaining part of old 66 still in existence, it's actually signed and maintained as AZ-66. The stretches between Kingman and Topock, CA (going through Oatman) and the one in CA going through Amboy are probably the next longest ones.