Hagi is a good place to explore by bicycle and there are plenty of hire places, including one at the youth hostel and several around the castle and JR Higashi-Hagi station. The best is Smile (22-2914; 3000 Shinkawa Minami; bike rental 1hr/day ¥100/800; 8am-sunset), to the right as you leave the station.
A handy bus system takes in Hagi’s main attractions. There are east- and west-bound loops, with two services per hour at each stop. One trip costs ¥100, and one- /two-day passes cost ¥500/700. Pick up a schedule at the tourist information office.
From Hagi, the JR San-in line and Rte 191, the main road, pretty much hug each other and the coastline up to the prefectural border with Shimane-ken. If you’re going to Tsuwano, there’s a direct bus from Hagi, but if you’ve got a JR pass you’ll want to go by train up the coast to Masuda, then change to the JR Yamaguchi line for Tsuwano.