Probably too late for the OP, but my husband and I are also beginners and just got off a cruise ship where we dove in Cozumel and Grand Cayman. Both were amazing diving. I would not skip either. We also dove in Key Largo before boarding the ship.
Having said that, trying to book dive trips off a cruise ship was a pain in the ass. So many rejections!
Even where the dive op was willing to accommodate cruise ship divers, many of them are on a schedule and are just not able to accommodate cruise ship schedules. In the end, we did end up finding someone to take us in both locations and I highly recommend them.
Cozumel - We dove with Tres Pelicanos. They have a regularly scheduled afternoon dive that leaves at 1:30pm, which fit into our ship's scheduled time in port (11am-7pm). Our ship docked at Punta Langosta pier and we just walked off the ship and to their shop, which was very close by (5-7 min), and from there they drove us to the marina. After the dive, they dropped us off in front of the pier and we just walked back on the ship. Easy peasy in terms of logistics. We also hired a private DM for a very reasonable cost and it was so worth it! It took the stress out of the dive for us immeasurably. They have fast boats and our DM was great! We dove at Palancar Gardens (beautiful coral formations, lots of large lobsters, gigantic turtles...just amazing) and Punta Tunich (drift diving, less coral formations but plenty of fish). We maxed out at 75 feet at Palancar Gardens and 60 feet at Punta Tunich.
A few thoughts about drift diving and current in general...some say it is difficult for beginners, others say it's the easiest diving ever. From the point of view of a beginner, it is a little scary...the current is strong enough to sweep you past your DM and you need to swim backwards HARD to get back to him! So your finning technique needs to be better than bicycle kicks and you need pretty strong legs and be relatively fit if you ever end up in a situation where you need to swim against the current. I can imagine some beginners might begin to panic if they aren't able to control where they are going. My husband and I were "ok" with it, but it does take getting used to. Our DM was strong enough to hold us both in one place so we could look at something in a crevice without floating off!
Grand Cayman - We dove with Off the Wall Divers. They were willing to change their schedule a bit to accommodate our ship's schedule. Our ship was in port from 8am-4pm. We were able to book the first tender as soon as we got on the ship but I guess this would depend on the ship. They sent someone to pick us up 5 minutes from the pier - we were at the North Pier. They drove us to the dive shop/dock, where we boarded the boat and dove at In Between and USS Kittiwake. The In Between was a wall and beautiful. Kittiwake was much larger than I expected. Both were very enjoyable dives. We maxed out at 100 feet on the wall and 60 feet at Kittiwake. The water conditions in Cayman were so calm and visibility was so good that the 100 feet wall dive was much easier and much less scary than the 30 feet dives we did at Key Largo just a few days earlier. I really loved the easiness of diving with this operation. You sit at the back of their boat, they literally put on the bcd for you, help you clip it up, put on your weight belt for you and you just stand up and giant stride in. No walking around on the boat all geared up risking falls. After the dives, they drive you back to the pick-up point.
