Black Hills great rides include:
--Needles Highway
--Iron Mountain Rd
--Wildlife Loop in Custer State Park
--Nemo Road and Vanocker Canyon (drops down into Sturgis, but is best ridden up the canyon out of Sturgis)
--Spearfish Canyon
--Road from BelleFourche to Alladin to Devils Tower to Moorcroft

You already listed Chief Joseph Hwy and Beartooth -- these are absolute musts that should not be missed!!!!!

To get to Cody, you might consider riding through the Big Horn Mountain in northern Wyoming. Beautiful country with lots of geological insights. Buffalo to TenSleep or Sheridan to Greybull or Lovell (NOTE: Major construction on a 10-mile stretch from Burgess Junction to Greybull).

Trail Ridge Road is magnificent, but there are just too many cars on the road these days. Try to cross early morning.