Reality check...
$1000 will get you a nice
week on Cayman - maybe...lol And I'm not talking in a vacation rental. House there regularly rent in the upper thousands per month. And many of the condo complexes are weekly - if they can fill them now why give them to you cheaper?
Plus food is absurdly high, gas isn't cheap - about the only thing on your list is that dives do run about 2/$100 on a package. There are some shore dives there - at most you rent from the on-site operator. CI$ are fixed at .80 to the US$ so you're 20% down on arrival. It's not uncommon to pay $50 for an average dinner. Even KFC was pricey. It's really a $2500/month place minimum. And I'm being optimistic. More if you actually want to eat. 1st or 2nd most expensive place in the Caribbean I've been. Food in the markets is shockingly high also. Not a lot of other things to do there either, butterfly farm, botanical gardens, kayaking, Seven Mile Beach activities are about the highlights. Downtown is cruise port central, there can be up to five ships in town daily - good time to be elsewhere.
Utila is sort of a tinier version of Bonaire - without any shore diving. Boat dives would be under your budget, staying in town would be affordable. You won't/can't rent a car - no need since all of town is one main road maybe a couple miles long. Everything else is scooters/ATV's. I'd be bored to death there after a week.
Maybe consider Roatan instead. You should be able to find something on/near the water for $1000/mo. Look on vrbo.com in the West End, West Bay or Sandy Bay. Dives are 10/$300 in the West End at a dozen dive shops. All boat diving there also - the only shore dives are on private resort property - if you're not a guest. Although it would probably only take you about 2 weeks to see all the Roatan attractions also - it's a pretty short list.
Lots of bugs on either island also if that's a consideration. Most of the beaches are infested with sand flies and Malaria shots aren't a bad idea. Food options are reasonable, a good meal is $20. In the West End they also have local food trucks daily with produce/fruit and fresh fish. It's nice stuff - we bought some. There's good food shopping in French Harbor on the other side of the island also - several large markets. Coxen Hole is mostly a place to visit during the day.
You can also go between Roatan and Utila for $100 R/T via the ferries if you wanted to check it out for a week or so. Roatan has decent internet access and Anthony's Key has a chamber if needed. The hospital was kind of dreary though - my friend spent a night there. Local people seemed friendly, I think the native population is Creole originally but most speak some English and Spanish.
Mainland Honduras is a pretty scary place - murder capital of the world - most suggest just getting thru it as fast as possible - even not leaving the airport unless necessary. So about all you'd want to do is maybe tour the Copan ruins some weekend - that's probably pretty safe. You can also fly direct to Roatan from the U.S.
What others have suggested might be a good alternative - Curacao. It's a larger island, cheaper and easier to get to from the U.S. They have the finest medical facilities in the region including a chamber. My friend owns there - lives here. She rents her house - I've sen pictures - similar to a decent 3BR/2BA home here - for $1200 month. In a normal neighborhood a 10min. drive from the beach. I've been to a food store nearby - prices were higher but not shockingly so. As compared to Cayman where we bought things for breakfast/lunch for the week and snacks and it was well over $100US.
I could find enough to do on Curacao to keep interested for a while. They have some real nightlife, bars, nice restaurants, beach clubs, a dozen or so casinos. Famous shopping district downtown, a lot of old history - some forts etc. Rif Fort is an old fort at the harbor entrance with a modern multi-level shopping center adjacent, shops, restaurants etc. Plus the old downtown is the one you see in all the pictures - the multi-colored buildings all are stores. There's also a farmers marked behind it and a fish market where you buy off the boats. Things like the Sea Aquarium, Ostrich Farm, Christoffel Park and unlike Bonaire there's at least 2 dozen really nice beaches.
Curacao - a unique Caribban Paradise
One advantage Curacao has over Bonaire is that almost all the beaches are also the better shore dives - many have a dive operation on site. The majority of the population is concentrated in town and east - west 1/2 hr. in Lagun is considered a vacation spot for the locals. Your 2/$100 boat dive converts into about a week of shore diving instead. Several times we saw a boat moored at a site we were shore diving - we did one boat dive all week and I felt like there were only 3-4 others I missed out on.
Curacao is the deep water port there so things are available. There's real stores for buying common things that might break during your stay. You don't see a lot of that on Bonaire although the food shopping has significantly improved over the last couple of years. Also even though it's the "C" island, it's actually between Aruba and Bonaire so cheaper/shorter flights to either.
If you want to see Bonaire - fly over mid-week and spend a week or two there. I've seen R/T flights in the $80 range - just not on the weekends. Bonaire runs on a Sat-Sat schedule. I guarantee you'll run out of thing to do by then - unless you're very easily amused. We did most of the highlights there on our non-dive day. People go there to dive their brains out as dr rich suggested. Some decent restaurants but prices are high there also - everything comes thru Curacao first. Bonaire is pretty expensive also - and pricier to get to originally. There's also bus service that runs all over Curacao - our apt. mgr. told us it's pretty reliable.
Go to any of the Bonaire websites - infobonaire.com or the other one and check the list of things to do there. One advantage to Bonaire is you can convert your 2tanks/$100 into most of a week of shore diving there also. And they're physically closer to each other than Curacao - many run back to back south of town.
There's just a
few shore dives in Hawaii also...lol - like 40 on Maui.
Scuba Shore Diving Region: Hawaiian Islands If you can afford it, it could be a good base - there's all the Maui stuff plus the ferries to Lana'i or Molokai - both of which are quieter. I sense that immersing yourself in the Hawaiian culture is easy on Molokai - never been there. Boat dives will run closer to 2/$130 though.
If you're staying in one place that long, you're going to have to look into the visa requirements and permitted length of stays.
That was my first thought when you mentioned your timeframes also. I think anything longer than 90 days requires a visa most places. And some proof that you're planning to leave - like a return plane ticket.
