Minehead is the terminus of the West Somerset Railway, a beautifully preserved heritage steam line that runs 20 miles inland through Watchet and Bishops Lydeard to a connection with the national network near Taunton. Trains run most days from spring to autumn, plus Santa specials in December.
The whole ride takes around 75 minutes one way, passing through the Quantock foothills and stopping at small country stations restored to 1940s and 1950s livery. From Minehead station you can buy a return and ride the round trip, or get off at Dunster (one stop away) to walk to the castle.