Hi DSR, we have been to both ports in the past and will do again this Feb. In Grand Caymen we have done the Sting Ray city snorkel twice and also enjoyed 7 Mile Beach as well. You can take a taxi to many locations that offer lounge chairs for a small fee and usually can find some food and drink as well. also, shopping is close to where the tenders dock. In Cozumel we have made it a shopping day (wife likes gold and bling) and do the strip for shopping and haning out. Penny will likely chime in with some of her great beach favorites. Enjoy !