We do a couple of things:
1) Throw money at them, starting salary of $250,000 plus a bonus multiplier of 0.5x to 2x gets you some very good candidates.
2) Emphasize these two things: http://www.cayman.com.ky/caymans-tax-free-status and http://www.weather.gov.ky/portal/page?_pageid=4421,1&_dad=po...
3) pay for trips home, give them $10,000 for travel a year and let them book their own flights.
Also it helps if this position is a set term, ie 2 years. I find having a definitive end date makes most things bearable as it gives people certainty about when their expat trip will be over. This is especially critical if there is a spouse or family that will be coming along with the employee.
Let people know that after their 2 year stint is up they are welcome to move to your head office if there is one somewhere else.
EDIT the salary and bonus I mention, only to make the point of paying well. The type of person we typically hire is very in demand, hence the pay.
Set terms is critical! Usually it does NOT end up being that important in the end, but at the beginning it can be very difficult to say "YES" to moving when you have six figure options that you always know that you can quit and walk across the street and get another well paying job. That's not the case on the Island I lived on.
On one hand, there are plenty of programming shops nowadays that are perfectly productive with all-remote or mostly-remote approaches.
On the other hand, I personally can't stay focused on work unless I'm in some sort of office, and I'm pretty sure I'm not alone. A company office is the easiest way to go about that, though office rentals and coworking spaces are a viable alternative.
Basically, there are arguments for either extreme (and all the increments in between those two extremes). It just depends on the team's preference.
I personally work from home, but time to time I do 1-2 week onsite visits. I find it really frustrating how people live like that - they just plan all their life around weekends.
I generally prefer snowy landscapes to tropical islands, but it's hard to argue with "tax free".
Having your head-office there is a bonus for employees who want to come visit.
You can do recruitment globally through hiring remote.
Test it out, you may find you get the best talent through offering both:
1) Either come live with us in the Caymans
2) Stay on your own island and work remotely
Moving package is a plus, too, and possibly offering assistance in finding a place to stay.