Jake,
Your best best will probably be on the West End of the island. You can do all of those things there with ease. We prefer the East End, but our approach to spending time in Grand Cayman is a bit different than yours. I will make a suggestion, however, and that is to stay at the Turtlenest Inn in Boddentown. That lies along the south shore about half way between the East End and the West End. It is a nice quiet place to stay with a very nice beach, good snorkling and, with the rental car that comes with your reservation, you can explore the island and do dives anywhere you want. However, it is not all-inclusive; so that may be a deal breaker for you. That said, we love staying there for a less dive-intense vacation. If you’re looking for big time night life... stay on the West End. If you want to relax and play the day by ear, I suggest Turtlenest Inn. There are many dive ops on the island and all are good... they have to be due to the competition. Any one of them could get you out to the Kittewake for an easy wreck dive. Hope this helps. KathyV should be along soon to provide more insight.
Look at Southern Cross little cayman, fantastic or incredible or outstanding or exceptional or possibility best in Carribean diving. All inclusive but really good food. Bungalows with outdoor showers, honeymoon suite with outdoor loo. Quiet, laid back, true barefoot elegance. Small resort with a big heart. Our favorite place in carribean. P.m. me for more info. Bill and DeeDee
Unfortunately, at this late date I don't know if you could even find accommodations over New Years on Grand Cayman, and if you do find something it would be very, very expensive. New Year's Eve is said to be lovely on GC and everyone watches the fireworks from the beach; but things book up way in advance and they are very pricey.
There are not many all-inclusive resorts in the Caymans, mostly hotels and restaurants and lots of condos, and some small (nice, clean, air-conditioned) diver-dedicated AI resorts with onsite dive ops. But you can arrange diving from wherever you stay. If you find a place on the West Side and Seven Mile Beach, the dive ops will pick you up in a van and drive to the marina - or they will pick you up by boat on the beach. If you stay at a more out-of-the-way spot, you may have to drive to the boat and there is rush hour traffic driving to the west bay area and George Town; so you would want to take that into consideration.
We love Turtle Nest Inn on Grand Cayman, but not for a dive intensive trip. We always do some diving on GC but these days we prefer relaxing and enjoying the topside restaurants and activities for a week on GC and TNI is great for us. But when we want to focus primarily on diving we head over to one of the sister islands of Brac or Little for a week at a small all-inclusive dive resort.
There are some terrific large hotels on GC, but New Years is at the height of the high season and hotels are likely to be crowded and expensive. A lot of people prefer to rent condos or apartments on GC so that they can prepare some simple meals and then go out for a great meal once or twice a day - but maybe you don't want to do any cooking on your honeymoon, and that is understandable.
You didn't mention budget but if price is an issue and you want to be on Grand Cayman, take a look at the Sunshine Suites on 7MB, it is across the street from the Westin but you will have full access to the Westin facilities, the beach, and their onsite dive op. You will have a kitchen at SS and can prepare some meals to help control costs. Not cheap but it puts you in the middle of the 7MB area at a cheaper price.
You could also look at Sunset House, nothing fancy but nice and clean and the grounds are beautiful and it has a great beach bar.. It is not on the beach but on ironshore, but breakfast is included and you have access to unlimited diving on the house reef, an onsite dive op, and you are close to George Town restaurants and shops.
Cobalt Coast is an all-inclusive with an onsite dive op and unlimited shore diving in addition to boat diving - but that area of the island is often winded out during the winter and you may not be able to shore dive on the house reef. It is on ironshore and they have a small, man-made beach and a pool. It is a nice place but low key and it is out-of-the way, so you will need a car to explore the island.
I agree that you should look at the sister islands. The Cayman Brac Beach Resort is a lovely small resort with good food and great diving and a gorgeous big infinity pool. The food is buffet but very good.
The diving is even better off Little Cayman and the Little Cayman Beach Resort is very similar to the CBBR - they are owned by the same family and have the same dive op (so is Cobalt Coast on GC).
Again there are not big, fancy resorts, they are clean and comfortable and friendly and they have good dive ops. Both the CBBR and the LCBR have lounging beaches but not swimming beaches. They have turtle grass and boat traffic. There are swimming beaches on the sister islands but if you really want a great beach, then Grand Cayman and 7MB is the best choice.
@wildbill9 mentioned the Southern Cross Club on LC, and it is smaller and more upscale than LCBR but more expensive, but that might be a very nice choice for a dive-centered Honeymoon.
Congratulations on your marriage and I hope you find a great place to celebrate the New Year and a new life together!