There is no one "best thing" to do in Cozumel. You would need to narrow down the possiblities by telling us more about your interests. We also need to know your comfort level with doing things on your own versus booking with the cruise lines.
Cozumel is a good place to do things yourself as they are easy to do. If you want to see Mayan ruins then that changes things as the big sites are on the mainland and I wouldn't suggest you try that on your won. Give us more info and we can help.
Thanks for your help Jim. We would like to do something easy like snorkeling or maybe snuba if it's not to expensive. I have found some websites that offer excursions but I don't know if it's better to book with them or the cruise lines.
Chankanaab Park, Cozumel Beach Resort, and Paradise Beach are nice places. Chankanaab has better snorkeling than the others. Paradise and Cozumel have nice ammenities and a nice beach. You can arrange for a cab ride and pay the entrance fees on your own. There are coupons available for some of the places on line, as well. We normally do things on our own, but have been to Cozumel many times. Like Jim said, if you want to go to Xel-ha or Tulum, it's best to book that through the ship. It's all about your comfort level.
For tours like snuba, I wouldn't hesitate booking a snuba trip online direct from a tour guide. Most are used by the cruise lines too. Just be sure you are clear on the date and if they refund you if the ship does not port for some reason. Any reputable tour guide company will do that. If they won't they are others that will.They will meet you at the pier so it is pretty simple.
If you want to do snorkeling only, then Penny's post is a great answer. We were just there on the Cruise Chat cruise and we took the whole group to Cozumel Club Caribbi. It was an all inclusive that included a pool, equipment rental and full facilities (and a freshwater pool) plus taxi ride for about half what the cruise ship was charging for a couple hours snorkeling. Just go out to the taxi lines and start asking around, you will find someone selling day passes. If you bring your own gear, you can just jump in a taxi and ask them to take you to Paradise beach...
Like I said, Cozumel is an easy place to do "on your own" Grand Cayman falls into that category too.
The Cozumel Club Caribe that we went to on the forum cruise was nice. It is north of town. The hotel was heavily damaged by Hurricane Wilma and they are converting it to condos. When we first drove up I got worried because the hotel looks like it was bombed out. However they have totally recovered the restaurant and beach area. For $20 we got round trip cab, and use of the facilities as Jim noted. Food and drink were extra but the food was very well prepared and the drinks also were nicely made. It was a very clean place and when I return to Cozumel I plan to return.
Thank you to everyone who has given me suggestion, plese keep them coming. Although my sister has not, I have been to Xel-ha, Tulum, Chichen Itza and Xcaret (which I would recommend to everyone) we are on a very limited budget. My sister has found a place to rent scooters for a reasonable price (although it will not compare to my Harley) and we are thinking of doing that and finding places to go on our own to snorkel. Keeping in mind that we are truly on a limited budget, does anybody know, if we do get scooters, where we should go?
Just a little back ground. I am a flight attendant, so even though I don't speak Spanish (yet), I am quite comfortable venturing out. I know that my sister likes snorkeling. I would like to step it up and take her to snuba or maybe to swim with the stingrays. Has anyone found a place to do either, that won't cost us a fortune?