Camp Long? But you have to do all kinds of stuff to be able to bring booze. I’d suggest Full Tilt but I think that 2 is a bit young. They are probably too young for bowling. The only places I can think of right now that would be good for 2 year olds are places where booze wouldn’t be allowed. The Y.
I’d suggest looking into a restaurant. I’ll have to think on it a bit.