score:8
There are only four airports in Japan that have direct flights to the continental US: Narita/NRT and Haneda/HND (Tokyo), Centrair/NGO (Nagoya) and Kansai/KIX (Osaka). None are particularly close to Kyushu, and it will probably cost you well over Β₯10,000 in train fares to get to your destination, unless you're going to slum it in local trains that take forever (not recommended).
Some alternatives: