"Super Hagi" buses connect Shin-Yamaguchi Station with Hagi (stopping at the Hagi Bus Center and Higashi-Hagi Station) every 2-3 hours. The one way ride takes just over an hour, costs 1600 yen and is not covered by the Japan Rail Pass (and the other JR passes).
By regular Bocho buses
90 min
¥2090
Bocho Bus operates 1-2 buses per hour between Shin-Yamaguchi Station and Hagi (stopping at Hagi Station, the Hagi Bus Center and Higashi-Hagi Station). The one way trip from Shin-Yamaguchi to Hagi costs 2090 yen and takes about 90 minutes. The Japan Rail Pass (and other JR passes) are not valid on these buses.
By train
Hagi can also be reached by train via the JR Sanin Line, however, service along the Sanin Line tends to be infrequent, slow and rather inconvenient:
From Shimonoseki, the trip along the JR Sanin Line by local trains takes about three hours, costs 1980 yen and usually requires one or two transfers of trains. Alternatively, from Asa Station on the Sanyo Shinkansen (only served by Kodama trains), you can get to Hagi by JR Mine and Sanin Line in about 100 minutes and for 1170 yen (to Hagi Station) or 1340 yen (to Higashi-Hagi Station). One transfer is required at Nagatoshi.
Above fees and schedules are subject to change. Be sure to check current yen exchange rates.
Getting around
Although there also exists a Hagi Station, Hagi's main railway station is Higashi-Hagi Station. The latter offers more services and is located somewhat more centrally than Hagi Station.
Hagi is best toured by rental bicycles as it is just slightly too large for convenient exploration on foot, although good walkers will be able to manage. Rental bicycles are available in front of Higashi-Hagi Station and other places across the city. Rental fees are typically 200-300 yen per hour or 1000-1500 yen per day.
Another option to get around Hagi is by the Maru Bus, a loop bus service for tourists that connects the stations with all the city's major sights. There are two lines, the West Loop and East Loop, which each operate every 45 minutes between 7:00 and 17:30. One ride costs 100 yen regardless of how far you travel. A 1-day pass for unlimited use of the Maru buses on one calendar day is available for 500 yen and a 2-day pass for 700 yen.
Tourists intersted to visit multiple of Hagi's historic residences note that there exists a combination ticket for 310 yen that provides admission to nine of the residences across the city, including the Kido Residence and Kubota Residence (but not the Kikuya Residence) in the former castle town, the Yukawa Residence and Katsura Taro Residence in the Aiba Waterway district and the Ito Hirobumi Residences near Shoin Shrine. The combination ticket is valid on one calendar day and can be purchased at any of the covered residences.