Short answer: Dawlish is better in winter than summer. Waves break clean over Brunel's sea wall as the trains come through, it costs nothing, and the station sits on the seafront if it turns unpleasant.
Level the whole way, with the sea on one side and the railway a few feet away on the other. Watch from behind the wall rather than on top of it, and never turn your back on the water — waves are not evenly sized and the big ones arrive without warning.
Half a mile south along the sea wall — sandy, sheltered by cliffs, and empty in winter. The best beach in Dawlish and most people never walk that far.
Still on the stream through the middle of town. Free, two minutes, and works in any weather.
Coryton Cove is the sheltered option and much the better entry than the town beach, which is steep steps down to pebble until the tide drops.
New Year's Day swims on this coast are organised by lifeboat crews, surf clubs and pubs rather than councils, and most are announced in the last fortnight of December on local Facebook pages. Check there rather than expecting a listing.
If you are getting in: the sea is colder on 1 January than at any point in the summer, cold water shock is the real risk rather than the temperature itself, and it is worth going in with people rather than alone. Walk in, do not dive, and get warm clothes on quickly afterwards.
Almost everywhere opens later than usual on New Year's Day, and some places do not open at all. Ring in the morning rather than assuming.
The station sits on the seafront, so you can step back onto the platform if the weather turns. Few places on this coast let you watch a storm from shelter.
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