Let KAYAK do the searching
Based on KAYAK hotel searches, the most popular destination is Salzburg (30% of total searches to Alps). The next most popular destinations are Cortina d'Ampezzo (24%) and Chamonix (24%). Searches for hotels in St. Moritz (21%) are also popular.
KAYAK users have found double rooms in Alps for as cheap as $42 (Salzburg) in the last 3 days. The average price is $463.