I just got back from my first cruise on the Fantasy about a week or so ago and we didn't go through Carnival. We didn't book anything ahead but we did plan on going through carnival. We decided to just do something in Cozumel and just hang out in Progresso but when we were in Progresso we were wishing we would have picked an excursion so for 10$ a person we took a tour of the mayan ruins and it was wonderful. Then in cozumel we rented a buggy for 45$ for the whole day, went to one of the beaches and had lunch and swam, went horseback riding for a half hour for 20$ and then drove back to the market area to shop.
Doing it by ourselves was waaay cheaper and it was nice just to be able to do our own thing and not worry about staying with carnival. The buggy was especially nice, being able to explore cozumel on our own was one of the funnest things ever. At first I was worried about being first time cruisers and going off on our own but my boyfriend and his uncle took care of everything and when I go with my family in June I plan to do it the same way.