On the tram system around Nagaskai, Ekimae (literally - above the station) stop, which is numbered T27 and reachable on both route 1 and 3 tram services, is the stop to get off for the JR (Japan Rail) Station. From here you can get local trains to Fukuoka/Hakata above 2.5 to 3 hours away, from where you can get Shinkansen (very fast trains) to the rest of Japan, including Tokyo (8 hours). It is expensive and even more so if you wish to get there quicker by express train.