Makeshift Litter Box
Your cat isn't suddenly going to start using the toilet in your hotel room (some cats can use the potty, but it takes months of training). You're going to have to bring her bathroom facilities with you. Instead of schlepping along your regular litter box, bring a smaller or disposable cardboard version that will serve the same purpose. Just make sure the box has a waterproof lining so you don't have to clean the floor underneath. You can also do the environment a favor by choosing a recyclable litter box.
When it comes to litter, the flushable kind is best for travel. Your hotel housekeeper won't appreciate you leaving kitty's little "presents" in the bathroom garbage cans.
Just because your cat uses a litter box and not a tree trunk doesn't mean that you can drive or fly all day without stopping for a potty break. Whenever you stop to use the restroom, let your cat out of her carrier and put the litter box on the floor of your car so she can do the same.
Bring along a litter scoop and plastic bags in which you can dispose of her droppings, so you won't be driving all day with the aroma of "eau de kitty litter" wafting up from the back seat. And bring a roll of paper towels and a box of wet wipes to clean up any accidents that may occur along the way. Cats who aren't happy about their situation may express it by purposely missing the litter box.