Although there are numerous beaches in Cozumel, there are only a few right near the port. You have to take a taxi to other beaches on the island. Sunset Beach is closer to the port than other beaches along the coast. Dzul Ha is just a little ways south of Sunset Beach. Chankanaab National Park Beach is located south of downtown. This beach may interest you more. It has a Mayan village, botanical garden and lagoon as well as. Playa Uvas is another beach within 15 minutes or so of the port.
For more info, see our feature Cozumel Port Guide