I wish there was an indoor equivalent for cats. I live in an apartment building that only allows 1 dog or cat. So my cat, Ember, gets no feline companionship. She used to enjoy playing in the hallway with a neighbor's dog, a Shih Tzu, but they moved away.
Yesterday, some maintenance people were doing some work in my apartment so I took the cat outdoors in her carrier to get out of their way. I set the carrier on a bench and had a book with me to read. Several people out walking their dogs stopped to check out the cat. She loved the attention, especially when a little half Chihuahua/half Pomeranian took a real liking to her and hopped onto the bench to touch noses with her through the carrier gate. She purred at him.
If there was an indoor place for cats, with cat trees, toys, water, etc. and permits with vaccination requirements, I'd take her there. But there's nothing like that around here. I think that it would need a supervising employee, too, to check permits and supervise the people as well as the cats.