Let KAYAK do the searching
Based on KAYAK hotel searches, the most popular destination is San Pedro de Atacama (51% of total searches to Atacama Desert). The next most popular destinations are La Paz (19%) and Arequipa (15%). Searches for hotels in Ica (15%) are also popular.
KAYAK users have found double rooms in Atacama Desert for as cheap as $10 (Arequipa) in the last 3 days. The average price is $109.