If you want it to be a riding vacation, then you need to read Motorcycle Journeys Through the Alps & Corsica
by John Hermann. The Dolomites are spectacular.
If you want to see more of Italy, then staying south of the mountains is better. Milan is a modern, industrial city, good for world-class shopping. Florence is fabulous and everyone should go there at least once. Pisa is small and charming. Rome is also amazing, but has a lot of big city feel to it. It has the busiest airport, and is worth at least a couple days on either end of your trip. Naples is less interesting, but Pompeii/Herculaneum is worth the trip south. Haven't been to Venice (yet) but it gets glowing reports. There are also numerous smaller towns and villages you can stay in and have a great time.
But before you rent a bike (or a car for that matter), be sure of your riding skills and comfort level, especially in the larger cities. I learned to ride in L.A. traffic and have ridden in many European and Asian countries, but Italian traffic is just plain nuts. You will have trucks, cars, bikes, scooters, and pedestrians coming at you constantly from all sides. We usually parked the bike at our hotel and either walked or used public transportation to go see the sights. I'm not saying that it can't be done, but don't underestimate this aspect, especially on an unfamiliar bike.
Riding/driving further out in the countryside is less hectic and the scenery is incredible. But you will need a GPS with local maps, whether in the cities or countryside. Street signs are erratic at best, and often the signs at an intersection will all point back to the same town that you just left.
And as when travelling anywhere, be extra vigilant with your belongings. The tourist sections have generations of pick pocketers trained to prey on confused tourists. It only takes a second to really mess up your trip.
Other than that, Italy is a wonderful place to visit. The food, wine, and scenery are all amazing and I would love to go back given half a chance.