Hi, not really, I did not go to St Pete Down Town very often. I usually go to "Fort de Soto park" and there is not much there but the amazing beach, and birds. If you drive to St Pete, you also have to go there
In Tampa you might want to have a look to Lettuce Park and walk along their wood trails along the river. I LOVE IT.
In down town Tampa, nowadays, the
Tampa Museum of Art | is a good place to go. Not because of the museum collection which is pretty much a shame, but because of the building itself and around it. There is a nice playground for kids, nice environment and nice sceneview of Down Town and on the University of Tampa.
There is also the small botanical garden of USF in Tampa. Weird place because of the way it is organised and because it is very small, but interesting and not as far
Enjoy!!