I can assume you will be on a Carnival ship for the day in Cozumel. The Puerta Maya pier area has PLENTY of shopping right off the pier. Anything and everything you could want is there. Many shops are the same as the ones in Punta Langosta shopping mall. I can't say anything about the beach, but when you go back to get on the ship the shops are there for you to spend your hard-earned cash!!! I did buy a conch shell from a cart vendor at the pier area, so look around and you may find a vendor selling shells.
2007 Victory & Triumph
2008 Conquest & Liberty
2009 Valor, Freedom, and Splendor
2010 Glory and Liberty
I gotta go where it's warm.....
Over 40 victim of fate.....