Your right about the whole bikinis = underwear thing. Might as well be the same thing. But if theres a bunch of kids around in whatever park and gals are doing this I think its a little wrong. Leave it at the beach. (And yeah I know kids go to the beach to, but still at least you know what to expect there.)
I don't see anything wrong with it, not that i would do it as i hate hot weather in the UK so sunbathing isn't really for me.
But i can see why people do sun bath in the park cos its not like we have nice beaches here is it lol