N.S.
We went to two birthday parties this year at the pet store! The store has a room in back where the kids can have cake and pizza. The kids got to play with the dogs, cats, bunnies, hamsters etc. The store clerks were very knowledgeable about the animals and the kids got a tour first. They even got to learn about the fish. They got to touch a snake, cuddle a guinea pig and play. The store gave out coupons in the birthday bags. It seemed like a weird idea when I first heard about it but it was great! You might want to check with pet stores in your area.
Also, some martial arts studios do birthday parties. Gymnastics facilities are another one.