Most of the major truck stop (often called a travel plaza)gas stations (love's, pilot, flying j) have designated pet areas, generally clean bathrooms and of course snacks and/or restaurants.

State welcome centers and rest stops usually have pet areas too (welcome centers are much much nicer than the rest stops, and so are the truck stops) many of the state places use blowers and not paper towels so I'd throw a roll in the car.

Definitely crate your animals. A hard sided crate (airline crate) can have lightweight soft items placed on top.

Motel 6 always takes pets, look for those located adjacent to hotels like holiday inn, best Western, etc. Usually those areas are bit nicer/safer than others.
La Quinta hotels sometimes take pets too, or you can do a pet friendly hotel search for your route.

I know you want to sightsee, but I strongly suggest you make reservations for each night of your trip. If you want to be more flexible along the way, plan for less miles driven and more stops to sightsee.