Let KAYAK do the searching
Based on KAYAK hotel searches, the most popular destination is Como (36% of total searches to Italian Alps). The next most popular destinations are Zermatt (28%) and Chamonix (22%). Searches for hotels in Cortina d'Ampezzo (14%) are also popular.
KAYAK users have found double rooms in Italian Alps for as cheap as $46 (Limone sul Garda) in the last 3 days. The average price is $510.