If you want to travel the Route 66, and it is a too boring, always stubborn to follow the road, you can install some detour in the route.
In some detours major detours are necessary, other trip is only a few miles from Route 66, and these can be taken on the road no great effort.

I once compiled the most important trip for you, they are again sorted by states.

• llinois – Amish County + Chicago
• Missouri – Ozarks, Jefferson City, Meramec Caverns
• Kansas – Dodge City
• Okloahoma – Wichita Mountains Wildlife Refuge, Alabaster Caverns
• Texas – Palo Duro Canyon State Park, Caprock Canyons State Park
• New Mexcio – Kasha Katuwe Tent Rocks, Las Vegas, El Malpais NM, El Morro NM, Madrid
• Arizona – Sedona, Grand Canyon, Monument Valley
• California – Joshua Tree NP, Death Valley, Calico Ghost Town, Las Vegas, NV

Decide yourselves, which trip you want to plan your Route 66 journey.

From a small State Park to the Grand Canyon National Park and Las Vegas is much here that could interest you as well.