Estonia is in the EU and pretty close with the US, too. But a very attractive country, business-wise.
Yeah, Estonia is in the EU, but a nice country.
Some of these may work: Switzerland, Monaco, Andorra, maybe Panama? I'm sure theres a bunch more, but I have never seriously looked into it.
Switzerland won't hand out a citizenship for money, though. Not sure about the others. I guess, betting enough in Monaco's casinos will earn you a passport sooner or later.