It is unlikely that you (exclusively) be allowed to choose the dive locations. But all of the spots on your list are fun.
We were typing around the same time, but I was slow. Scuba Du has that list as their published schedule.
we will most likely at least shore dive every day
Ok I see that idea mentioned by new divers a lot. I never understood that approach as I always planned on boat dives, but it comes up for some reason. And I suppose that you could justify using the time and money it'll take for you all to travel and be there even if you missed much of the best of Coz. I'm just guessing there are two of you, going for a week - so with prudent shopping you might have used the Orbitz discount to get air & hotel packages for less than $500 each for the week, so shore diving there would be better than not being there those days. But dang you will miss so much that way; the really good diving is from boats only, on the southern reefs not close to shore, in the marine park where you can't dive without a permit and DM even if you figured out a way to get out there.
Then there is safety to consider. If you boat dive, the DM is there as a guide, not a handholder - but if something were to go badly, a possibility to always keep in mind in this adventure sport, then the DM and Captain are there to help you, radio for additional help, etc. In comparison, if you're shore diving and something goes wrong -
you are on your own at least until you get back to shore.
Don't think you can have problems? I have between 400-500 dives and I still find ways, often of my own making. I've never been carried off in an ambulance, but I have seen other leave that way 6 times. I trust you have at least the mid level or top level DAN dive insurance, not the cheapest dog plan?
By the way, Coz is not exactly beginner diving like the reefs of Key Largo - where I went for my first dive trip. If this happens to be your first, I really suggest hiring a private DM for the two of you on the first boat trip. Small amount of money well spent on learning safe drift and boat diving. Many new divers have managed without that approach, but it's still a very good idea.
And even if you don't like my private DM for a day idea, the first time you do dive a wall - do ask your boat DM to explain what to do if you get caught in a down current. Not common but they happen at Coz and you need to know in advance; he'll explain.
How did you pick Scuba Du? Are you staying at the Presidente? Surely not as you wouldn't spend that kind of money then skimp on boat dives, but there is not any shore diving around that part of the island that I've heard of. If you are staying at some other southern location, then by the time you take a cab up to Villablanca area with your gear, rent tanks from an operator up there, then cab back with wet gear - that's half the money of a boat trip even at Scuba Du rates but not half the fun. No help with gear, no drinks, no fruit and facial towels, nothing.
Maybe there is more to your plan than I am guessing here? You can try shore diving the second day, maybe even the first day afternoon - but I doubt that you'll do it more than once. My guess is that you'd have a better trip if you just planned on boat trips every morning, but let me know how it works out on return. I'll watch for trip report from you I hope.
But if you'd like to tell us more about your trip plan, some of us might offer more insight and suggestions.
What are the "must do" dives? The wife has just put the finishing touches on our trip so we should arrive next Monday evening and stay for about a week. She is a non diver, but I'd like to at get in as many of the must do dives that I can. I haven't been to Cozumel in over 15 years and I didn't bother to log my dives then.
Some of the names in Lax's post ring a bell, but still foggy. I do remember a drift dive where we were in and out of a few swim through holes that was a blast.
Thanks,
Couv
Really, I've long forgotten how many times I've been to Coz but I seldom ask where the boat is going, never the first couple of days - just that they don't stick me on a newbie boat. The operators I dive with usually asks for preferences and discuss. Even tho Scuba Du does
publish a daily schedule, I bet that changes with weather conditions and maybe with divers boarded. If I don't screw up the first day, get plenty of rest that afternoon after leaving my house at 1 or 2 am the previous day, then I may start requesting wall dives, and by the third day I might request Cathedral (not Devils Throat! Done it twice not! Don't want to see that boring cave again!) but I really don't care much where as long as we go. So many good sites to dive, and I don't mind doing the same one twice in a week. Once we requested the same dive twice on the same trip as we all had Nitrox for our second tanks and liked the dive that much.