I suspect in most of the countries in EU you can go without visa for 3 months - your US passport grants you a tourist visa. When you go to another country, you

I suspect in most of the countries in EU you can go without visa for 3 months - your US passport grants you a tourist visa. When you go to another country, you get a new visa for that country, which means that you could stay in Europe for a while by going to a new country every three months.