It depends if you are specifically looking for a large resort with the fancy pools and many services, or just the sorts of things you mention. The resorts on LC are small and quiet and not the same kind of experience as a big place. Each one is different in what it offers but you can get the same sorts of things you mention, all-inclusive with good to great food, on a beach, great dive service where they take care of stuff. You might find you enjoy a place on LC. In Belize, besides Lighthouse there is Turneffe Island Resort, I haven't been there but have heard good things.
On Grand Cayman it is surprisingly hard to find a place that's really nice with everything convienient in one spot. The big resorts and other complexes along 7 mile beach are not generally dive oriented with good dive facilities and ops right on the spot. There are smaller places that are dive oriented, but much less fancy. Cobalt Coast on GC is small but nice, on the water but no beach, dive oriented with a real shop and shore dive right there, but you will do a fair amount of gear handling as the boats don't leave from there and the better shore dive is at their other shop. The food is pretty good but I wouldn't do a whole meal package there as the menu will get old, and it's not a long drive to many good restaurants.
Morritt's and the Reef on the east end of GC are pretty nice, I especially liked the Reef Resort (all beachfront) as a place to stay. There is not an actual dive shop at the Reef, more of a t-shirt shop Ocean Frontiers operates. You would go next door to Tortuga Divers at Morritt's or down the road to Ocean Frontiers real shop where the boats leave from. Ocean Frontiers will pick you up and is all about service and handling your gear for you, actually more than I prefer. They just opened condos right at Ocean Frontiers called Compass Point, they seem nice enough but it's more a dive resort rather than a luxury resort. As far as eating, I'd avoid the restaurant at the Reef it was lousy (and not open early enough for breakfast to make a morning dive boat, nothing is.) The food at Morritts was surprisingly good. There are a few very good restaurants within about 30min drive for dinner, but it's the sort of place where since you have a condo anyway, you'd want to buy groceries and eat at least breakfast and maybe some lunches in your condo.
I often recommend Young Island in St. Vincent to people looking for a nice place to stay. It's a bit of a pain to get to, but a wonderful unique resort, good all-inclusive dining and service, good diving, Dive Saint Vincent will handle all gear and it's very convienient diving for someplace that's not a typical "dive resort." Not a place where you'll get to do 5 a day if that's what you want, 2-3 is more typical.
There are some very nice places in Turks and Caicos on Provo, long boat rides to the good diving but Caicos Adventures is a great op with a gorgeous boat, they will pick you up at your hotel and take care of your gear.
