I know the Barnstaple 'henge' (which made me laugh) and the wickerman, which I thought was temporary and would gradually fall apart but I assume it is regularly renovated. I also have a fondness for chalk hill carvings, like the Long Man of Wilmington, Cerne Abbas Giant (genitals and all!) and the Uffington White Horse, but I am not sure whether they are public art or ancient monuments, nor whether it matters.
I like the point about Banksy, perhaps his is the purest form. Public buildings are sometimes terrific and probably public art - I suppose it depends on how you define art; there are some who would reject anything the purpose of which was primarily utilitarian as art.