There is nothing to speak of in Calica. You will need to take a cab to somewhere nearby. My recommendation would be to take a cab to the Omni Resort in Puerto Aventuras. They have a great pool and beach, with a nice beachside restaurant and bar. We had chips, salsa and fish tacos. You could also explore Playa Del Carmen
In Cozumel there are lots of places to eat, I can't think of any that I'd really recommend though. Maybe someone else will have something to offer.