Wonderful, friendly Italy is too large a country to see in one visit.  A first timer would probably desire to see mid-country: Rome, Florence, Pisa and maybe Venic, or the south: Amalfi, Capri, Naples (Pompei) and Sorrento.  
This being my fourth visit to Italy, after doing the south, mid-country and Sicily separately, we decided to fly into Milan and concentrate on the region called Emilia Romagna which included the towns of Parma, Modena, Bolgna and Rimini, and the independent country of San Marino.  
We rented a car in Milan and motored to Parma, famous for its cheese and posciuto ham.  Modena, famous for Luciano Pavorotti, neighboring Busetto for Toscanini and Rimini right on the Adriatic Sea, famous for its miles and miles of beaches.  I couldn't take advantage of the beaches being October but the weather was in the 70's.  Outside of Rimini we visited San Marino and San Leo, two high-up mountain communities with small winding streets and breathtaking vistas.  After Rimini we turned in the car and took a three hour train ride back to Milan for three more days. The train service is efficient, comfortable and modern; we booked first class just to get reserved seats.
We spent the last three days in Milan, one of the top fashion capitals of the world.
You can get lost wandering in Milan and get an excellent meal, lunch or dinner in any out of the way cafe` or restaurant.  One paricular interesting street in Milan is Via Dante.  It is a pedestrian street with outdoor cafe`s, shops and street entertainment.  And of course the Galleria in Milan, the covered outdoor mall is teeming with restaurants, shops and people.
Unfortunately, La Scala, the most famous opera house in the world was closed as the season does not start for a few months. 
Italy has many historical, cultural, educational ande festive venues.  It is a must visit for anyone who has not been there.  And lastly, Al Italia Airlines is one of the finest, efficient air line of the world.