It's very hard say what part of Italy is the best for a tourist If you have a nice budget Milan, Rome, Bologna, Venice or Florence are ready for you (Florence is the second best italian city for me ). If you are looking for a genuine city Neaples is ready for us! You need a beach? Taranto have the best beach of italy for me.. but we have some great beach around all Italy, Sardinian and Sicilian sea is great too.. another lovely place for have a "summer-holliday" in the Costiera Amalfitana, a lovely place very near my house .
Are you looking for the peace of the mountains? The Dolomiti, in the north-east are ready for us.
If we exclude Italy you have a lot of possibilies, here some tips for us: Dublin, Lisona, Marsille, Montecarlo, Monaco, Berlin, Helsinki, Prague, Bratislava, Wien and Reykjavík (the city of my dream since I was a kid)
Good luck in your future European holliday!