Where are the best places to spend 3 extra days in Europe using the rail system before going to Venice?

We fell in love with Italy while visiting Rome, Florence, Venice, & Genoa a few years ago and want to do something different for this trip. We used the train as our means to travel so we got to see a lot of the countryside. This time, we have a 12 day Greek Isle cruise departing out of Venice. Our plane lays over in Zurich, so we thought we might get off the plane there instead and jump on a train and see some of Switzerland (and maybe part of Germany) then meander our way down to Italy - perhaps spending only a night at each destination or maybe staying on the amalfi coast. We like to travel fast and see as much as possible! We have a total of 3 nights. Any 4-5 star hotels, points of interest, cities to visit or recommended itineraries would certainly be appreciated. We plan on purchasing a 3-country train p.