The provincial capital is an easy morning out from Ban Krut: a bay, a monkey temple and the best seafood market on this stretch.
Find a room before you go.
Prachuap Khiri Khan is seventy kilometres north of Ban Krut on the same coast and the same railway line. By car it is an hour on Phetkasem Road; by train it is a little over an hour, and much prettier, but the timetable does the deciding because only three services a day stop at Ban Krut.

Most people who stay in Ban Krut do this as a day trip: up in the morning, the market and Khao Chong Krachok before it gets hot, seafood by the bay, back in the afternoon.
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The nicest way, and cheap, but tied to three departures a day from Ban Krut. Check both directions before committing to a day trip.
Phetkasem Road north the whole way. A scooter is fine in daylight; the highway carries a lot of lorries, so keep left and take it steadily.
Local services run along the highway, but they leave you at the Ban Krut junction ten kilometres from the beach. Fine if you are patient, slow if you are not.
Step-by-step transport guides for this stretch of the Gulf coast.