Typically high season in the Caribbean starts around mid-Sept thru mid-April/May 1st. There are obviously exceptions. Sometimes it's a big increase other times just a few $/day since they seem to just be taking advantage of the trend. Look at any dive resort website - most list high/low season rates/dates.
Cozumel, Roatan, Utila, probably Belize then Costa Rica is probably low to high from LAX. There's some pretty reasonable flights to Cozumel and quality reasonable accommodations - nicer AI resorts also. From Cozumel you can also do day trips to the mainland via the ferry or even some of the dive operators. One offers an all day trip to the ruins at Tulum paired with dives/lunch. I think it's Scuba with Alison but I'm not positive.
Roatan is cheaper than Utila because the flight over to Utila often originates on Roatan. Or San Pedro Sula on the mainland. Typically that flight runs around $160pp. Alice at Worldwide Travel on Utila can arrange that. She has a Facebook page with current details. Or you can do both ferries from Roatan - takes about 3-4 hrs. each way since both go to the mainland at La Ceiba. Either island has similar prices on everything else - there's just a lot more of it on Roatan.
Utila mostly consists of a mile or so town with just about everything clustered together - some houses in a couple areas farther east/west or the 2 decent AI resorts on the south side but both are accessed via boat only. It's a big backpacking destination so there must be some trails - there's one short peak also. A big part of the island is mangrove lagoon and there's a LOT of bugs. A woman in our group went birdwatching - she looked like she had chickenpox a day later. It's pretty quiet there - nightlife is mostly DM trainees in the bars at night. And you want to stay away from the "thump" if possible. Try something farther west - there's some decent resorts about 15mins. walk away. I've actually only seen it from the water but Coral View Beach resort looked decent. And they have a shore dive and a pool. Most have golf carts or bikes also.
Utila Official Site - Utila, Tropical Island Paradise for everything. Here's Alice's info:
https://www.facebook.com/wwtutila/
Good diving - there's some deep wall diving off the north side. Some larger pelagics also - we reliably saw sharks once a day or more. If you plan your trip for early spring, there's a good chance to swim with Whale Sharks on snorkel trips most operators do after diving. We did with 8 over 2 days.
Roatan is just more of everything. More resorts, more AI dive resorts, West Bay is a very nice beach. There's ziplines, some hiking - there's one lower peak there and it's more hilly in areas. The West End has most of the shops, restaurants and bars/clubs. The south side is more AI dive resorts and all going east are pretty isolated by distance. Many people go to Cocoview for a week, get shuttled there, dive, eat and never leave. We personally like the West End since it's all walkable. A nice place there is Cocolobo but there's many others. You might also consider Luna Beach Resort - it's about 10 mins. walk/water taxi from town and they have a pool, decent beach, breakfast/lunch etc. Dinner is a walk to the West End or water taxi to West Bay. One option there is they rent their "treehouses" to single couples if available. Costs a little more but you get a 3br nicely upscale villa located above the resort on the hill. If you want more of a dive resort, Anthony's Key is currently offering a BOGO - I'm sure I saw it's extended into 2016 also. Nice resort, get an overwater cabana on the Key for privacy - the pool and small beach are also there. If you tire of the resort bar/food - the West End is about 5mins. by cab away. A lot of the West Bay properties are also beachfront.
Bonaire is really going to be about diving. There's not much else to do, maybe rent a bike one day. The Donkey farm is fun once. Drive down and see the Flamingos/Lighthouse once also. It's still a pretty small, quiet island although there is some cruise traffic now. And it's pretty expensive to get to. If you want waterfront - the dive resorts all book at PP rates including diving/truck rental so that can be a little costlier. It's cheaper to find a water view resort or property in town across the street from the water - all will also have a dive package option. We stay in condos south of town with their own dive operation on site - downside is we drive for every meal we don't cook. They're not really budget priced either. Bonaire is also a desert island so hiking is going to be among cactus etc. - and pretty warm leading to hot in the summer.
Bonaire Offical Site - Top Destination for Diving and Eco-Activities for details.
An option not on your list might be Curacao. It's a much larger island than Bonaire but the same diving (50 miles apart - same reef). Much more to do there non-dive - Christoffel Park is mostly hiking trails and there's a short peak to climb also (walking) Same diving, easier entries than Bonaire. One advantage to either is that if you buy a $100+ shore dive package that's all it will cost you. One other advantage to Curacao is the dive sites are almost all sandy beach entries with facilities, food, even dive operators on site. On Bonaire once you leave the dive resorts you're pretty well on your own. And Ironshore entries. Hate to see you get cut-up/break something on the honeymoon. Curacao is also a deep water port so everything is cheaper than Bonaire since most of it comes from there. Food in Bonaire stores/restaurants was pretty high - on Curacao not much more than a large metro city in the U.S. Also some of the flights to Bonaire stop in Curacao first - to fly over costs around $160 r/t so that's in your Bonaire flight cost also. I can also get to Curacao by 2PM leaving Phoenix very early in the morning. I can't get to Bonaire till 7PM or so. Unless you do the Friday night red-eye through Houston.
Curacao, a unique Caribbean island paradise. Official Curacao site for details.
You could also split your Belize time differently than I suggested. There are some mountain ranges inland and there's a mayan city ruins near one. So maybe do a few days on Ambergris diving then a few days inland. Plenty of "adventures" river running, ziplines, cave tubing etc. I don't have a good reference for that except Blancaneux Lodge and it's not reasonably priced. It is in the same general area though. This post and my post above are pretty much all I know about Belize - we'd planned to go there but changed to Roatan instead since we found a better deal in the West End for everything. We look for diving and some nightlife as a group though.
