Fort Desoto Park, just south of St. Pete Beach, is consistently rated one of the top beaches. There is also a county park on the beach at Sand Key (just south of Clearwater Beach) and Caladesi Island is another great park (accessible by ferry). The county park beaches are really nice, quiet, and well maintained.
If you're looking for more action, either Clearwater Beach or St. Pete Beach would fit the bill.
Count on at least a two hour drive to the Gulf side.
We either go to Sand Key (Gulf Side) or Cocoa Beach (there are a couple parks well south of the pier that are nice and quiet).