Singapore: probably meets all of your requirements. Low tax, easy to open a business, lots of private schools. No idea how to rate the hospitals, it has a couple in the best hospital lists in the world, but I don't trust those. Drawback is everything is expensive.
Andorra: not cold for Northern European standards. Low tax, a couple of international schools, private medicine, you should be able to access the private medical system in Spain. A few inconveniences are no train, no airport (closest are Barcelona and Toulouse), custom inspections into France or Spain, generally isolated feeling and tourist centered feeling.
Portugal: Warm and friendly people with good food. I don't know anything about the schools or medical system. Bureaucracy probably isn't great. Low tax for a couple of years. Unfortunately local citizens do not benefit it so a foreigner taking advantage of it is likely displacing a local. Feels very unfair.
Puerto Rico: not cold, no US federal taxes. If you are a US citizen and non-resident and move there, there are some other tax benefits, but people who were already residents can't take advantage of it. Lots of infrastructure problems.
From the list Puerto Rico looks to me like the new idea. I was considering the others, yes. But Andorra is cold as hell and boring :( Portugal's bureaucracy approaches that of Spain, but Spain is getting sooo bad IMHO that some day Portugal could be better, if it is not already.
Thanks for the ideas!
A few other low tax places to consider that I don't know much about: Belize, Bulgaria, Croatia, Macedonia.
As for the negative points... did you listen to their english? lol.
And Dubai? Yes, it is not too cold there, hahaha.
- it is not cold, if possible - the tax rate is low (even if I have to pay services later myself but with my own choice) - the hospitals and school system are good, even if private - it is not difficult/expensive to open a business
I am all ears :)