Established as the smallest national park in the Bahamas in 1959, 1.5 Acre Peterson Cay is a tiny uninhabited island surrounded by beautiful coral reefs.  Naturally the main attraction is snorkeling.  Most people reach Peterson Cay by a boat or kayaking tour - it is only accessible by boat.  Kayaks can put in off of Barbary Beach, while boats usually will leave from Port Lucaya Marina.  You can take a private boat there as well.  It is located about 30 minutes from Port Lucaya by boat.

The coral reefs are some of the most beautiful on Grand Bahama, making for nice underwater seascapes, but fish life is not as robust as in other reefs on the island.  You'll want to visit at high tide, as immediately from the beach the water is very shallow at low tide.  If you snorkel from the beach and all you see is some soft branch corals, keep swimming out - the main reef is a little ways offshore (not far, but you don't see it when you first enter the water).

As with all National Parks in the Bahamas it is illegal to remove any shells or other artifacts from the park boundary - in the water or from the island - and this is strictly enforced, so don't do it.   Make sure to leave no trace so that the next people that visit find it to be as pristine as you did.