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.
We loved Xcaret when we were there last summer....I thought the underground river sounded really great (although, I was afraid the water would be too cold and wouldn't go) But I'm going to next time...2 of the teens with us went and said it was great. And you only notice the cold water for a few minutes then you get used to it...
The taxis take U.S. dollars. Playa is just 4 miles or so away from the dock. The stated fare for 4 passengers was 80 pesos last time I was there - about $10 if you include tip. Make sure you agree on a price before entering the cab. Playa Del Carmen is a small town. 5th Avenue is blocked to traffic so you have to walk to it. Just get out of the taxi at their stopping point and you'll pretty much be just a few steps away.