I only wish I could add to all of these interesting places here; mine was a little more mundane--my high school. We played mostly in classrooms, but for a six-month period we actually played in the science lab (the then-sponsor took us on when the second sponsor, an exchange teacher from Australia, didn't want to do it anymore; our first sponsor was the "real" sponsor.). We tried to see if we could play one session "under the stars" in the school's planetarium, but was turned down.
We only had a few ideas for a good playing space:
>> Lots of blackboard space;
>> A place where the club could bring in food and drink;
>> A place where no-one would be disturbed by "noise";
>> The sponsor was always welcome to join in.
His rules were even fewer:
>> Don't break anything (remember this was normally a chemistry lab!);
>> Keep the noise down;
>> Clean up after yourselves at the end (including erasing all of the blackboards--they were large!).
It worked out very well--I only wish we could've thanked him for putting up with us; I often wondered what HE thought of US.