Let KAYAK do the searching
Based on KAYAK hotel searches, the most popular destination is Kagoshima (57% of total searches to Kagoshima Prefecture). The next most popular destinations are Yakushima (29%) and Kirishima (7%). Searches for hotels in Amami (7%) are also popular.
KAYAK users have found double rooms in Kagoshima Prefecture for as cheap as $10 (Kagoshima) in the last 3 days. The average price is $150.