What are some free (or nearly free) places for groups of 20 or more people to meet regularly?

If there is someone in your group who lives in an apartment building, see if they can use the recreaction center. Usually, apartments rent them to residents at a very low rate, or in some cases, nothing at all, if you leave a check as a deposit and clean up afterwards. You have plenty of privacy. If there is a small fee, bring a pot luck dinner and let everyone contribute a portion of what they would have spent at a restaurant.