In the past we have been to Tabyana beach and had a great experience. Carnival's port and nearby beach however do not compare and left us disappointed.
Excursions were cancelled due to weather and there were no attempts to reschedule them when the weather improved. Research suggests not leaving the port on your own so we opted not to leave the ship as there's not much to see or do at the port.
Cozumel is always great and you can do many different things here and feel safe. Carnival's excursion prices however haven't expensive.