Hi! Hubby and I recently relocated from Alabama to Washington State with our two cats. This is what we did. At first, I tried "crating" them in the car, and I'm talking about one of those really big pop up cubes, big enough to comfortably hold a big german shepherd type dog, but my older kitty couldn't stand it, he howled and howled till we let him out.
So, that being said, we simply let them lose with us in the car. My younger kitty stayed mostly curled up in my arms all day. The older, well, he enjoyed roaming around the car and even sometimes wanted to help dear husband to drive
I kept their litter box, covered with a big garbage bag, on the back seat and each time we stopped, I simply took the garbage bag off and they used. After they used, I would shake their food dish and they would eat. I gave them no water to drink during the day. It went very very smoothly, much better than I had thought.
We stayed at Best Westerns, Comfort Inn's, and I think a Day's Inn. In any case, we were upfront about having the kitties with us and there were no problems. Most places charged a small pet fee of $10 - $20. One place charged us a $100, but refunded us in the morning after seeing there were no damages.
Whatever you do, don't try to "sneak" them in. If you do, and get caught, the hotel could hit you with a $100 fee. That's what we were told. One hotel we stayed at, actually had a no pet policy, but we lucked out. The receptionist happened to be outside having a smoke and she spied me and the two kitties in the car. Having pets herself, she took pity on us and let us have a room for the night.
One more tip, so you don't have to load and unload the car each night and morning, make sure to pack an overnight bag with what you will need over the next couple of days and have a bag with your cat food etc. handy so you don't have to carry a lot.
Also pack with you, paper towel, always comes in handy, small garbage bags to dispose of kitty waste neatly, some Nature's Miracle stain & odor remover, Just in case
and just leave the room as clean as possible so that us folk that travel with our pets don't get a bad rep!
Hope this helps!