The rooms are not too small, some are bigger than others so you may call ahead to check. There are some tighter spaces depending on the room.
There are a lot of variables: How you define small? Would a crawl space be over whelming? How many people will you be with? All of this will make a difference as it will affect your mental ability to cope when locked in a room. I'd ask for the escape room with largest amount of space and then limit the amount of people you take with you if this is something you REALLY want to do.
I feel that even someone with claustrophobia can enjoy the spaces comfortably, but then again, I do not have that condition and it's only my opinion.
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