1. Playa de las Estrellas, Isla Colon
Playa de las Estrellas means Beach of the Stars in Spanish. And starfish are indeed abundant in the glassy waters of this Panama beach (also called Starfish Point). Located at the far northern tip of Isla Colon (the Bocas del Toro archipelago's largest island), Playa de las Estrellas is accessible via public bus or "collectivo" shuttle from Bocas Town. Although Playa de las Estrellas is can't-miss, for laying out you'll want to walk to the nearby Panama beach, Bocas del Drago.
2. Red Frog Beach, Isla Bastimentos
Located on Isla Bastimentos in Panama's Bocas del Toro archipelago, Red Frog Beach is one of the most popular Panama beaches with the backpacker crowd. The island's unique rainforest-in-miniature setting results in some of Panama's richest island biodiversity -- including the Panama beach's namesake, the red tree frog. The area is (rightfully) protected; entry is $1, and the beach is a short walk from the drop-off point.
Not many travelers make it all the way to the San Blas Islands in Panama's northeastern Kuna Yala district, which is a shame. Many of the most pristine island beaches in the Americas are located in the San Blas archipelago -- in fact, almost every island is ringed by a sugary strip of white. Popular islands (well, popular in Kuna Yala terms) are Isla Pelicano, Dolphin Island, and Isla Robinson. Carti is a great destination for those who want to sleep in a real Kuna village; although the beaches aren't great, stays include tours to nearby San Blas beaches. Note: most accomodations in San Blas are the most basic of basic -- huts and mosquito netting -- and meals include whatever the sea provides that day.
4. Taboga Island, Panama Bay
Near Panama City (on Panama's Pacific coast) the beaches aren't spectacular, but Taboga Island offers several wothwhile ones. Located in the Panama Bay, the island is just a quick ferry ride from Panama City -- perfect for those who don't have the time to travel all the way to Bocas del Toro. The island is rich with local history (pirates! conquistadors!); you can find an overview on Destination 360.