If you like coastal scenery, you could also take the Sanin line all the way from Shimonoseki, but this adds another hour. You need to be careful to plan the connections well (both trains average about once every two hours), but if you do, this is about the same time as the bus from Shin-Yamaguchi. Then take the Sanin Line to Higashi-Hagi Station (half hour). From Asa take the Mine line to Nagatoshi (1 hour). Asa is only serviced by Kodama trains, and it is two stops from Shin-Yamaguchi Stn and also two stops from Kokura, which is much more well serviced.
If you want to take the train the full distance to Hagi, you'll want to take the Shinkansen to Asa station. The train link to Hagi from there is about 2 hours, but you can get there faster by taking the "Super Hagi" bus to Hagi (see below). Many Sakura and a few Nozomi trains stop there. The closest Shinkansen station is Shin-Yamaguchi. From Ube, take a bus to Shin-Yamaguchi Station in Yamaguchi and connect via bus from there (see below). Yamaguchi Ube Airport (UBJ) in Ube is the prefecture's largest airport, with regular flights to Haneda Airport in Tokyo on JAL and ANA (about 90 minutes).Shuttle buses run from the airport to the city (80 minutes). Hagi-Iwami Airport (IWJ) has one flight per day from Haneda ( Tokyo) and Itami ( Osaka) on ANA.If you're staying overnight, they can arrange delivery to your hotel while you explore the city. Many Meiji statesmen were born and raised in Hagi, such as Hirobumi Ito, the first Japanese Prime Minister. In the middle of the 19th century, the ChÅshu allied with the Satsuma Domain to deliver some long-awaited payback, toppling the Tokugawa shogunate and thereby spurring the Meiji Restoration - and, with it, the modernizing of feudal Japan. The Mori clan transferred the capital of the Choshu Domain ( Choshu-han) from Hiroshima to Hagi at the same time, where it remained the political center of the region for over 250 years. But it was not until 1608 when the Mori clan, exiled here after a humiliating defeat by the Tokugawa shogunate, built their massive, imposing castle at the foot of Mt. The first castle in Hagi was built by the Yoshimi clan.