I'd love to do something like this, but ideally for a shorter time (with a team), or more informally (with more people).
Renting a house in Hawaii (ideally one set up for startups; with some extra cars, high speed Internet, printer, whiteboards, etc. all set up) for a month might be a good way to do a 2-3 week project kickoff, followed by a week long vacation for friends/family.
I'd still love to find a group of (security? infrastructure? bitcoin?) startups which have a reason to be in non-USA which move to a place like NZ/HK/CH/IS/EE and operate. One of the advantages of SFBA is you can switch companies very easily. Moving for a single company to a place like Costa Rica doesn't do that.
3 months is in the range where it is long enough to feel permanent, but too short to really set things up properly, unless you have a yearly cycle among 4 different locations or something.