Let KAYAK do the searching
Based on KAYAK hotel searches, the most popular destination is Fukuoka (96% of total searches to Fukuoka Prefecture). The next most popular destinations are Kitakyushu (3%) and Kurume (1%). Searches for hotels in Itoshima (0%) are also popular.
KAYAK users have found double rooms in Fukuoka Prefecture for as cheap as $16 (Fukuoka) in the last 3 days. The average price is $95.