There is always Meagans Bay if you want to go to a nice beach, very easy to take a cab there. Even better though, get over to St. Johns/Trunk Bay, good snorkeling and the beach is like a postcard, well worth the time and effort getting there, you certainly have enough time. There are also ship excursions that take you there, among a few good other excursions. We did "BOB" there once, great time, something a little different, but you'd need to book that very early, it fills up quickly. Be sure to allow a little time for shopping there, you can even pick things up at the mall by the pier, same stores that are downtown.
another vote for St. John - the beaches are beautiful and the snorkeling is very good.
Go in the morning. Great info at www.vinow.com
Hire a cab for a few hours after the beach to just tour the island
take the Paradise Point Tramway to a high point on the island for a breath taking view of the harbor.