Top dive op recommendations: Most dive ops including these will pick you up at the Palace, you'll have to check idividually with them to see about overnight storage. Also e-mail the Palace or check thier website, and ask see if they have them.
Blue Angel: (our current dive op), fast boats (most should have new motors by now), great, attentive DM's and captains. All experience levels catered to for sure.
Dive with Martin: Long time Coz favorite, we used them for years. again, fast 6-pack boats & very good DM's. I very much enjoy diving with Orlando and David, great personalities as well as good divers.
Bottom time divers: Operated by Raul Plates. Raul is one of my favorite Cozumel DM's, very safety minded and is extreamly good at finding critters. As far as I know he is still just a one-man operation (+captain of course), so personal attention just comes with the package.
Speaking of personal attention, last and certainly not least is BlueXTSea: Christi and crew run a top notched, "boutique" dive operation. If it's pampering you want, this is the way to go for sure. Fast boats & Very highly thought of DM's here on the SB.
Welcome to the family & congrats on the "Nups", personal note, don't just get stuck at the buffett at the Palace, venture downtown and get some of Cozumel's wonderful local flavor.
whoever you choose for a dive op, make sure and let them know of any requests or concerns you have about diving and AGAIN when you get on the boat in the morning, let the DM's know your experience level and what you are comfortable doing...you will be very well taken care of, all these guys and gals are there to make sure you have a good time and usually do an excellent job of it.