I am wondering what the best way to get to Fukuoka is. Could I fly to KIX or NRT and then take a train or some other method of transportation from there? How else can I get there, flying to F U K seems to be quite expensive.

You can fly into KIX and then take the train -- it is about 4.5 hours, including one transfer at Shin-Osaka station. This is only "cheaper" than flying into Fukuoka if you are planning on doing other train travel in Japan. The cost of the Shinkansen (bullet) train one way would be $250 or so -- but with a Japan Rail pass you could nearly get a week long pass for not much more than that. Train travel is the was to go in Japan -- please check the other current Japan trip report on this forum.