Cozumel could be a very good choice. The diving is great, it's easy to get to, and it is a lot of fun. Some might question whether it is good for new divers, but lots of people get certified there. Much of the diving is moderately deep (50-80 feet) and there is current on most dives. If you don't fight the current, but just drift along with it (I say it's lazy-man's diving, just kick back and watch the reef go by), it is really pretty easy. I did all of my early diving in surge and current, so it seemed pretty easy to me. You won't find the same kind of diving in shallow, still water that you would find in Bonaire, or Little Cayman for that matter. But if you let the dive op know your level of experience, you shouldn't get into anything too challenging. The town is lots of fun, with plenty of good restaurants. You can also take the ferry over to Playa del Carmen, which has good restaurants and bars and some more nightlife. There are some Mayan ruins on the island, a good little museum in town, some shopping, tours of various sorts, and a park at the southern end of the island I have yet to visit.
Playa del Carmen and the rest of the Riviera Maya, the area south of Cancun, could also be good, although the diving is not nearly as good. There are some very nice hotels and resorts all through the area, everything from backpacker places on the beach to little inns to boutique hotels to all-inclusive to mega-buck luxury spa resorts. There is a lot going on in Playa, it's somewhat quieter in most other locations. You fly into Cancun and take ground transporation to your ultimate destination, so it's easy to get to.
Grand Cayman is very developed, I would say over-developed. We have only been there on layovers on the way to Cayman Brac and Little Cayman. Seven Mile Beach is non-stop hotels (you can't even see the water from the road) opposite a series of US-style strip malls. I hear the East End can be nice and the diving is good all over Grand Cayman. It depends on what you are looking for.
For a honeymoon you might consider St. Lucia, particularly Anse Chastenet resort. The island is a beautiful volcanic island, reminiscent of Hawaii. There are lots of things to see and do. There is a rain forest and a volcano. You can go hiking, fishing, sightseeing, etc. Anse Chastenet is a very beautiful and romantic resort. I think it would be a great place for a honeymoon. We might have gone there, except that my wife preferred a non-diving trip and we went to Paris. The diving is pretty good in St. Lucia, but not great. I think it is well-suited to new divers. Anse Chastenet has an excellent dive operation. It is not very easy to get to St. Lucia, but if you fly out of Miami, it wouldn't be as bad as it is for us coming from Detroit. It's not cheap, but if you are thinkging of Hawaii, I would guess that this is a possibility. I would enthusiastically recommend it as a honeymoon destination and I would give it a qualified recommendation as a diving destination. I guess it depends on your priorities. If diving is clearly your top priority, you may want to go someplace else.