Visas: Are you US citizens? If so you won’t need visas for a stay of less than 90 days almost anywhere in Europe. Only exceptions I can think of are Russia and Belarus. Turkey may still require a visa, but that’s easy to get on arrival in Turkey. There’s a visa checking tool pinned to the top of the “Cheap Flights” forum.

2 week feasibility: Does your 12 days include flights to/from US? If so, you’ve only got 9 1/2 days on the ground in Europe and, IMO your trip is way too rushed. Spend a little time plotting this out with the train schedules at: Http://reiseauskunft… and a calendar. Plan average of 3 days per city and for 12 days I would try to limit to a total of 2 (max 3) overnight trains and intra-Europe flights. If you have 12 full days in Europe you might be able to handle 5 cities that are relatively close together. I see two options based on your interests: Option 1, Save Italy for your next trip (when you can spend 10 days there) and concentrate on London, Paris, Amsterdam and add somewhere else (the Rhine Valley, another stop in France, Brugges, Belgium) in Northern Europe. Option 2 would be to spend the time in Italy. Plan Rome, Venice, Florence and a less urban stop like Cinque Terre, time in Tuscany or perhaps a single stop in Switzerland or Southern France.