I don't think I'd call BASFA meetings unstructured. If we were one of those many fun groups which just wanted to get together to socialize, pizza places would be excellent. But I'd rule them out as conducive to any kind of meeting where business is conducted.

It's a tough job, finding a venue which meets all of our needs. But there are lots of similar groups (Lions, Rotary, Optimists, Toastmasters) which have the same requirements, and I'd dropped a hint at the start of our search that contacting those kinds of groups for clues might be useful.