Short answer: Honestly, Lynton and Lynmouth are hard to reach without a car — there is no station and bus services are limited. Once you are there, though, the cliff railway joins the two villages and the Valley of Rocks is a walk from Lynton.
Lynton and Lynmouth are on the edge of Exmoor with no railway and limited buses. It is one of the harder places in Devon to reach without a car, and it is better to know that than to be stranded.
Bus timetables in Devon thin out sharply from October and differ between summer and winter. Check the operator's current timetable before building a day around a connection, and check the last bus back before you settle in.
The cliff railway joins the two villages — water-powered, running since 1890, climbing five hundred feet in about two minutes. Between that and your feet, you do not need a car inside the villages at all.
The Old Bank and the Greenhouse in Lynton, and the Ancient Mariner in Lynmouth, are all walkable.
If you want Lynton and Lynmouth without a car, staying a night or two makes far more sense than a day trip. Arrive, then walk.
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