Chankanaab Lagoon is a few miles south of town (about $7 by taxi), much closer to there the cruise ships dock. It can be quite crowded, as many ships offer the park as a land excursion, and many people on land/air holidays visit as well. It is a decent place to snorkel in spite of its crowdedness, as Cozumel's shore is "ironshore", jagged and rough, and only hotels and (crowded) resort beaches (Playa Sol comes to mind) have sandy beaches.
Chankanaab has lots of attractions, incuding an "Archaeological Trail" worth the walk. There is a "jungle trail", and a botanical garden. You can get a bite to eat or a drink here, and rent snorkeling gear. (If you have a mask and snorkel of your own, so much the better- a well-fitting mask makes the experience much nicer.) Some ships arrange snorkel trips on large (and crowded) catamarans for a half-day. They usually go to nearby Palancar Reef shallows- nice, but again, crowded.
A good excursion can be made to the Maya ruins here, at San Gervasio (about $16 by taxi). You can take an excursion, or hire a taxi for the round trip and a wait (be sure and arrange the before you get in). Take water, it can be quite warm. Entry is about US$3 per person, and there are guides on site you can hire. These ruins are not as imposing as Chichén Itzá, or even Tulúm, but they are interesting. The Maya people used to make a pilgrimage here to pray for children, or to thank the goddess Ixchel when they did have a child.
Birding can be fairly good too. "Cozumel" comes from the Maya "Ah Peten Kozumil", "Island of Swallows". There are good restaurants downtown (La Choza for Mayan / Yucatecan food, El Capi Navegante for seafood, Morgan's for upscale dining, Prima (on a funky rooftop!) for northern Italian and superb beef and local King Crab, and Guido's (aka Pizza Rolandi) for a nice pizza in a relaxing courtyard. There is also a very nice, if basic, museum that highlights the ecology of the island. (Note: the downtown has been taken over by the usual stores you see in every cruise destination. Also, avoid buying items made of black coral or "tortoise" shell, both endangered.) You can buy decent silver here, especially that made in Taxco.
Also be sure to take some insect repellent, as mosquitos can bite on shore (daytime too). DEET 20- 30 % is best here at home, and you can buy "Aután" almost anywhere in Mexico- it is DEET-based also. (DEET higher than 30% can cause allergic reactions, and will affect synthetic materials and plastics; Avon Skin-so-Soft and Citronella may NOT work on all biting critters.) The "Riviera Maya" in Mexico, like much of the inshore Caribbean and some islands, has experienced (day biting) mosquito-borne dengue fever- as one who has had that, trust me that you do NOT want to share that experience.
Bon voyage, or more appropriately, ¡Buen viaje! José (near Sacramento, CA)