Cozumel is great for new divers--and more experienced ones as well. We love the Fiesta Americana because it is away from town, has a nice breakfast (buffet and menu), a nice dock where dive boats can pick you up, a great pool area for apres dive, and very pleasant rooms. You can reserve directly or go thru Island Dreams, a Houston company accessible by phone, fax or e-mail.
We have used the Dive House at the hotel and you can get a package from Island Dreams for the hotel and Dive House dives. The Dive House is very convinient since it is on site and has lockers near the dock for your personal gear. We have also dived with other "companies" and our favorite is the Manta Ray (La Mantaraya) whose owner and main dive master is Fernado Gonzales; Fernando is a fine dive master and a degreed marine biologist; La Mantaraya take out groups or six and fewer.
The absolute best restaurant in town is the French Quarter. Hands down the best food! There are lots of mediocre places to eat: generally, if they are along the main street fronting the harbor, they are substandard. We think they specialize in one-time tourists who debark from cruise ships and never return.
Cozumel is a great place--not as exotic as some Caribbean or South Seas locales, but great diving and pleasant people.
Have fun!