D.
I am in NW Bradenton. A good spot is Lewis park because it is FENCED IN!!! Very nice for young toddlers. It has plenty of shade. It is off of Manatee Ave in Bradenton- Behind Trinity Church (30Th St W and 1St Ave W). You may wish to contact SarasotaMommy.com they probably know the parks in Sarasota. I am D. with WhatsHappeningManatee.com and I can tell you all about the parks in Bradenton.
Take care
D.