I have visited switzerland, italy, greece,netherlands last year after entering germany WITHOUT ANY VISA. Yes you require a visa...to enter every country except germany but its so weird..once you are in europe, germany-greece is domestic flight..for them!
I was on the train from munchen, germany to zurich, switzerland and the police control came in the train..they looked at my passport and said "do you have anything to declare for swizterland?"...Mind you switzerland is not in schegen..and i enjoyed zurich.
THen i took the train from Zurich to Milano Italy and the italian police came on board 3 times....at 3 diff stops...all looked at my passport and didnt say much.
I came to NY from Milan, Milan->JFK and the immigration officer stamped my passport without even saying anything about the visa...
ITS NO BIG DEAL. KISS that document because it has u.s.a on it!..U.S has lot of meaning..its like gold as one officer put it.
Also i even was in France while I went through germany..the officer didnt knwo what document it was..and called someone and the guy said Germany doesnt require a visa for it..so he said where was I going.i said germany showing my ticket..and he let me go without any problems.
THe POINT is..GET A VISA IF YOU WANT but if i was you..I would go to germany and go through europe..if someone questions you,just say you didn't know...You have a legal document and are legally in a country..