Summer of 2015 I took a cross country trip on a bike. I left Niagara Falls, NY and completed ~4700 miles in less than two weeks. We rode through more than 11 states I believe it was and honestly the best was Colorado, Utah and the PCH in California. We stayed at a motel over night on the old route 66 and although it was similar to a ghost town, the accommodations were definitely tailored to tourists.
I'd recommend visiting the following that we visited (time permitting):
Pacific Coast Highway
Telluride, CO
Pikes Peak, CO
Lake Dillon, CO
Zion, UT
Grand Canyon
Moon House Ruins (Utah)
Horseshoe Bend, AZ
A spot we didn't make it to but wish we did was Havasu Falls in Arizona. But, from my understanding you have to hike into this place which you have to call months in advance to reserve a camp site as it's an all day affair. You'll also go through a small little village called Supai which gets mail delivered by mule - kinda neat.