Let KAYAK do the searching
Based on KAYAK hotel searches, the most popular destination is San Pedro de Atacama (50% of total searches to Atacama Desert). The next most popular destinations are La Paz (19%) and Arequipa (16%). Searches for hotels in Ica (16%) are also popular.
KAYAK users have found double rooms in Atacama Desert for as cheap as $16 (La Paz) in the last 3 days. The average price is $111.