If you want a combination of a romantic resort, a beautiful landscape, and some pretty good diving, go to Anse Chastenet on St. Lucia. The best diving on the island is all within a few minutes of the resort and the shore diving is great there. The diving is not up to Cayman or Cozumel standards, but it is worthwhile. The resort is very nice. If you are prepared to spend some buckage (which it appears you are), pop for one of the upgraded rooms. Each of them is unique and they have great views. The food is very good and the service throughout the resort is excellent, as long as you remember that you are on island time. Try to dive with Victor, he has been there for years and is an outstanding divemaster. If you want to emphasize the diving side, go to Little Cayman. The diving is spectacular and the island is practically deserted. There really is nothing to do but dive. Another cool option (I haven't tried this yet, but would love to) would be to charter a sailboat and cruise through the British Virgin Islands or the Grenadines. Some crewed charters offer diving and you always have the option to meet up with a local dive op. I think you could pull it off for the budget you mentioned. There could be lots of other options, depending on what you are looking for, but those three cover three very different ways to do a memorable trip.