1: I think you'll like the Mayan. We've been staying there every January for about 8 years.
2: The closest dive op is Aquaworld. They actually run the dive shop at the resort and their big marina is just down the road. I walk to the marina in the morning when I dive with them. There used to be a nice little 6 pack operation (Blue Peace) right there as well, but they seem to have moved away. A lot of folks complain about the cattleboat thing, about too many divers and too many "tourist" divers, and admittedly AW's boats are big, and there are certainly a lot of apparently inexperienced divers, but that's what you get in Cancun. The serious divers head for Coz and the cenotes. I like to think of myself as a competent diver, and I can go out with AW and still enjoy my dives as long as I accept that there will be some shepherding and babysitting going on. Fortunately there are enough shakey divers to keep the dm's occupied and they tend to leave you alone if you look like you know what you're doing. Don't be afraid to try them out.
3: The cenotes are awesome. You can easily hook up with a day tour to the Akumal area, about an hour away by bus. I think a day trip with lunch and diving runs about $150 but I'm not exactly sure as I haven't used that service for a few years. I'm lucky enough to have a friend who teaches cave diving in Akumal (when he's not exploring) and he drives up to get me when we're gonna dive. If you can swing it I think it's nice to get away from the group tours and do the cenotes with a small private group. That way you get a better variety of sites and your guides are likely to be the people who actually laid the line in the caverns originally. They can tell you more of the exploration history and what connects with what, etc.
If you aren't cave certed then you'll only be able to do guided cavern dives, but they're pretty exciting and you'll be hard-pressed to tell the difference between a good cavern and a real cave. Taj Mahal is one of my favourites but I haven't done it for a couple of years.
4: You can also do a day tour by bus to Cozumel for a day of diving. The last time I went (with AW) we stepped off the ferry directly onto the dive boat when we got to Coz. AW uses nice boats, albeit cattle style. I believe they're all Newtons in the 40-50' range. They make a nice stable spacious platform, even when there's a bunch of divers, and given the frequently bumpy conditions during the winter, the wide beam is kind of nice for those prone to mal-de-mer.
Hope you enjoy the holiday. I'll be at the Mayan for the first two weeks of January.
JF