I failed to mention Xel-Ha which is a bit south of the pier - around 25 miles I think. Beautiful place. Xcaret is pretty too, although I think people go a bit overboard in their praise of the place. There is a public beach on Playa del Carmen - the closest town - but it isn't anything spectacular and not especially clean.
Xcaret has a nice beach on a small inlet, among all it's other attractions. Please note that while they take dollars you often get your change in pesos.
For perspective, Calica is just the name of the industrial pier used by the ship. It is literally in the middle of nowhere and it is primarily used by cargo ships. They will have taxis, buses, and a tent city of souvenir vendors set up, but nothing else.