There are free public playgrounds all over the place - I just spent the morning at one near my parents' house with my friend and her young son. There are at least 3 or 4 playgrounds in my hometown (population 15,000) and dozens in the city 15 miles away.
You probably won't find many of them mentioned online though, as they aren't the kind of thing that is advertised on the internet (I can't find a mention of any of the parks I know when I do a Google search) - they are just small local parks in residential areas of towns.