Corbyn's Cove is the closest proper beach to Port Blair, a curved strip of sand backed by palms south of town. It is not the beach people cross the Andaman Sea for — Havelock and Neil are far better — but it is easy, breezy, and useful if you have a few hours before a flight or ferry.
Come for a stroll, a coconut, and a first look at the water rather than for solitude. Swimming conditions vary, so check locally before going in.