Sites are limted as far as accessible easy to find sites are concerned - Navarre Beach Pier and Pensacola Beach Reef. Both sites are shallow, less than 25', but contain lots of fish and other marine life.
Navarre Beach Pier is easy to find, its the big pier on Navarre Beach...
Pensacola Beach Reef is located ~150m off the beach directly out from where the restrooms used to reside(ask the lifeguards, they'll point you in the right direction). Its about 150-200, East of the new fishing pier
Fort Pickens offered a few sites, but its not accessible at the time as they've not completed the road back into the park.
Currents are typically a concern. Surf can be at times, but not so much lately. Expect water tempertures in the low-mid 80s F, wear some kind of protection from jellyfish.