The Wikipedia article here includes places with financial implications like bookstores and cafes. I don't see why these have to be excluded, for a long time a nearby pub was my "third place", I knew a lot of the people there and would share life with a lot of them for several years.

Where I live there are also plenty of free options, I play beach volleyball at a public field, meet at the local lake to swim, meet in the local park to play disc golf, meet at the Pumptrack meet at the skatepark and in the winter go backcountry skiing (ok there I have to pay for public transit)… and everything accessible by bike…

If there are no alternatives just talk to the major or so… I know two skateparks and a beachvolleball court currently beeing build just by locals in their freetime with the full support (also financially) of the villages major/council… if there’s no support… move :D (I already did this twice because I don’t like living in such communities)

Third places don’t need to be free. Wikipedia article cites bars, cafes, coffee shops, gyms.