I highly recommend George & Kathleen Bush Ltd. in Grand Cayman. (345) 949-3371 Cell: (345) 916-1750. They have a small boat (about 12 passengers; nothing fancy), low-cost, very knowledgeable, and very friendly. They took us to an area outside of "Stingray City" that was right by the reef and had plenty of fish and stingrays but no crowds! It was our first trip to the Caymans and we were somewhat leary about paying for the excursion at a roadside stand. It turned out great (they even made a couple of extra stops during the van ride so we could pick up an underwater camera and to look for a particular bottle of liqueur we were searching for.
In Cozumel, if you're just a bit adventurous and self-confident, I recommend renting a car and driving to the ruins on your own, then go to the west side of the island where you can park along the road and have a private stretch of beach.
Feel free to send me an e-mail if you'd like more details.