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Lisa Porter, CEO of a website that lists pet-friendly places to stay and activities across the country, said more businesses are catering to customers with a pet in tow than ever before. For example, vineyards and wineries have opened their tours to pets, and as many as 90 percent of hotels in some cities are pet-friendly, she said.

Most five-star hotels have accommodations and perks for well-behaved pets, and even most discount hotels, including Red Roof Inns, Motel 6 and Extended Stay America, are pet friendly. Other hotels have weight limits on animals. Some charge a nightly fee for animals, some have cleaning deposits and some will charge only if there is damage.

In France, where Ms. Long and Chula spend four months every year, so many people take their dogs to restaurants that there is an “under-table culture going on,” she said.

The French hospitality for dogs stops at museums, though: “The French prize their dogs, but they prize their artwork even more,” she said.

Chula has been such a good travel buddy that she inspired Ms. Long’s book, which is a travelogue written from a dog’s point of view. Ms. Long said having Chula around means never being lonely — partly because of all the people who stop to admire the dog.

“If you want to be a hermit, go [traveling] alone,” she said.