You can ask someone about going to Manzanilla and Mayaro on the south-east coast. It's got miles of coconut-fringed beach and is ok for bathing depending on the time of year. Now (May/June) is a very good time. But as it's on the Atlantic Coast, it's a little more wavy than beaches on the sheltered sides of the island (North and West).
Try Vessigny Beach, Granville, Columbus Bay and Icacos Point (This is the very south western tip of Trinidad). Ask about Puerto Grande, Erin, Los Iros, Palo Seco, Quinam and Moruga. None of these beaches are known as snorkelling spots but they are nice quiet spots. Just go with someone you trust who knows the area. Never go venturing out alone.
If you want snorkelling, you need to go to Tobago. But you can visit the Wild Fowl Trust while you're in Pointe-a-Pierre. There is the Devil's Woodyard which is a series of mud volcanoes. You can ask about the famous Moruga Hills or the Trinity Hills for which Trinidad is named in Spanish. There is wildlife sanctuary and reserve there and you can see monkeys, oppossums, deer, armadillos, ocelots and lots of birds.
Hope this helps.