Let KAYAK do the searching
Based on KAYAK hotel searches, the most popular destination is Tbilisi (55% of total searches to Caucasus Mountains). The next most popular destinations are Baku (30%) and Kutaisi (8%). Searches for hotels in Stepantsminda (7%) are also popular.
KAYAK users have found double rooms in Caucasus Mountains for as cheap as $9 (Tbilisi) in the last 3 days. The average price is $90.