My favorite city in Europe is Venice. The whole place is one giant museum. If you go to Venice, stay the night. It is a whole different experience once the day trippers leave. Also, see the sites around San Marco, but explore. Don't get stressed if you get lost...you are on an island.

No matter where you go, walk into the churches. The in situ art in Italian churches is off the charts....even the churches you have never heard of. You will walk into some church you have never heard of and it has a Michelangelo, Donatello, and/or Bernini piece inside.