Besides whatever other EU countries people here might mention, I know that Romania offers residency permits to US citizens who want to start a business, and the

Besides whatever other EU countries people here might mention, I know that Romania offers residency permits to US citizens who want to start a business, and the fees and taxes are fairly low. (If I understand correctly, you have to renew the residency annually, but you can still transition to permanent residency after five years like any other temporary residency class.) If you have a great idea, then you can start in Romania and enjoy the same access to the single market as anywhere else in the EU.