Playgrounds require you to have children with you - for example I don't think it would be socially acceptable for a group of unaccompanied adults to show up to a playground and sip some beers while they chat amongst themselves, like you might do in a public plaza in Europe.

Municipal parks, like the kind you can find in Savannah GA, are nice third spaces. But I think there are very few such parks in suburban America that are not also mostly playgrounds. I would not count nature reserves as real third spaces.