Thanks for all the responses. A couple clarifying points:
--- Probably the biggest thing we're looking for is a pro-business, pro-immigrant, pro-technology set of government policies. We want to live in this location for several years and be able to work without the government thinking that we're some sort of threat by doing so (the position the US takes, for instance.)
--- We're also looking for good infrastructure. This doesn't mean we'd rule out a hut on a beach somewhere. A latrine toilet would be ok if we had good broadband.
--- I did just ask for "Startup culture" but by that I meant that there were people who were entrepreneurial in the area, and maybe there are enough people who are programmers to have a monthly developers meeting in an area of interest to us. The whole startup culture thing is a bonus, and my asking the question was to get a read on other parts of the world-- but startup culture isn't the number one criteria for our choice, but it will help us narrow down if we have multiple good candidates.
--- We're not likely to need Venture Capital. We've got the equivalent of an angel round in the bank already. So access to capital is not that important. This is a business that will self fund and if we need capital to accelerate growth, that's not so hard to raise anywhere when you're already profitable.
-- In looking at these answers and looking at all of the visa requirements, I'm struck by the number of countries that would be happy to have us stay there for 90 days but then would put us thru the ringer if we wanted to stay there 6 months or longer.
I wonder if there is any country that values bringing in great minds who want to build something.