Hi,
Taking into account our solid experience doing cycling tours in the Alps and the Pyrenees, I would recommend you to fly to Milan or Venice (it depends which airport has better connections). If you are looking for a real the Giro d'Italia experience, you should stay in Bormio for a 2-3 days and Climb Stelvio on one day and on other day Mortirolo+Gavia loop. And you should definitely go to Bolzano direction and climb all iconic and most beautiful climbs like Passo di FALZAREGO, Passo FEDAIA, Passo SELLA, Passo GARDENA, Passo di VALPAROLA, Passo CIBIANA, Passo DURAN, Passo di GIAU, Passo di FALZAREGO, Passo PORDOI, Passo di COSTALUNGA etc. I would reccomend to stay in most central place Corvara In Badia Kurfar. You can reach almost all of those climbs by bike from there.
You are welcome to contact me personally. I would be glad to send you the bike routes you should ride. Or if you wish, we can guide you too. And even more, provide a full service for you. It's up to you. Please find a sample what we do here
http://www.hcbiketours.com/en/race-viewi...tour#ad-image-0