Cozumel, the largest populated island off the coast of Mexico, is a popular stop on many cruise destinations. It is known for Mayan ruins, reefs, and beaches. The biggest and best Mayan ruins are not on the island and require a long trip to the mainland, and most ports stopping in Cozumel will also stop at other ports with better access bigger ruins.
Many of the beaches are private, so it can be difficult to find a good beach that you can freely access. If you are willing to put up with a timeshare presentation, you can get in on a resort such as El Cid, which has a great beach with some pretty good snorkeling right off the beach.
Within walking distance of the port there is shopping and open air markets. There is a Mayan history museum.
Cozumel, thanks to less strict restrictions than in the US, has more impressive dolphin encounter programs than you'll find most other places. You can actually swim with dolphins, as opposed to standing in knee deep water with them as most programs in the United States offer.