We live in Sarasota, and I've grown up going to Myakka Park. The camping facilities are better at Oscar Scherer, IMHO, and Oscar Scherer is very close to the gorgeous beaches. However...Myakka is much bigger, you can rent bikes and take long rides, you can take the Gator Gal boat ride, there are hiking trails, there is a walkway out into the river where you can see birds, alligators, etc.
The best picnic area, I think, is called Clay Gulley, and it's in the back of the park. That's where we used to do Mother's Day each year.