Budget would be helpful. I did Maui and Kauai. I am reasonably well traveled for a peckerwood, and these two stand out for their beauty. The road to Hana and the seven pools etc are touristy, but the road hanging off a friggin cliff limits the crowds.
A trip to Rome would also be terrific. Few days in Rome, Rent a car if you are brave, or take a train ride to the Amalfi Coast. Positano, Sorrento, a day trip to the Isle of Capri. Amazing.
In Rome I recommend getting a car or driver and going up into the Roman Hills. I ate pizza at a place that opened centuries ago. It overlooked the lake formed by a volcano where The Romans practiced sea battle, over the city of Rome, and straight out into the Sea.
Also in Italy a trip from Rome to Cinque Terra. Last time I was there I drove from Florence to Cinque Terra, and visited Porto Fino, San Remo, Monaco, and Nice Paris. I just basically followed the coast and as it came close to dark, found places to stay. Most towns I visited I have never heard of. Just followed the sea. I would ask shop owners for a good place to stay and invariably one they or their relatives had a flat or townhouse to rent. I rarely paid over 100 euro a night. I did splurge a bit in France however.
I personally would not choose Cancun, Cozumel, Jamaica, Bahamas for a honeymoon. I know many do. I would think more towards Bermuda, St Barts, etc., but again, budget is an issue. I have been to all of the above places multiple times, especially when I was younger. Aruba was enjoyable and I finally put my weak windsurfing skills to the test. Lots of fun. On Aruba I was able to find a private beach for about 4 hours by renting a scooter and traveling to the north end of the Island. I also did the same in Cozumel close to the lighthouse but I guess that is probably developed by now. Had hours to ourselves on the beach with one old gnarly fisherman cooking fish over wood fire for maybe $5.
My advice? Just don't be to busy, or feel forced to "cram everything in", with an obvious exception for the honeymoon night! Take it easy, relax, get to enjoy one another. Congratulations.
Pwood