There are literally hundreds of beaches to choose from in the DR, but each area has its own character.
Beaches on the south-central coast, like Boca Chica, have relatively calm water, so they're good for families and snorkeling. Boca's proximity to Santo Domingo makes it convenient for those visiting the capital, but the beach is crowded with city dwellers, vendors, and plastic chairs during the weekends. On weekdays you have the best chance to enjoy the powdery sand and the reef-protected lagoon (the Caribbean's largest) in peace.
Northern beaches are the windiest, and are best for kiteboarding and windsurfing—though the islets around the Samana Peninsula, such as Cayo Levantado, are a tranquil exception. Cayo Levantado has fluffy sand and translucent, placid waters (and, between January and March, whale watching).
On the northwest part of the island, Playa Cofresi attracts serious tanners for its perfect sun exposure and bodysurfers and boogie-boarders for its excellent waves. Cayo Arena (also known as Cayo Paraiso) is a small island off the northern coastal fishing village of Punta Rucia, and makes a good day trip from Puerto Plata. The islet has a long spit of white sand, surrounded by shallow water and 250 coral reefs—fabulous for snorkeling. Cayo Arena Tours, based in Punta Rucia, offers daily trips.