Short answer: The arcades and the front give you a short wet hour. For a proper day, The Big Sheep is five minutes inland and The Milky Way about fifteen — both largely indoors, both with opening days worth checking first.
Westward Ho! is a holiday village built around a beach, and in the rain what is left is the arcades, the playground and the doughnut stands near the front. That is a wet hour with children rather than a day, and it is worth being straight about it.
The parking is £8 flat whether you stay one hour or eight, which makes a short wet visit poor value. Factor that in before driving over.
The Big Sheep is the nearest proper wet-day attraction — animal shows, indoor play, a rollercoaster and lamb feeding in spring. Check the opening days before driving out, as it runs a reduced timetable outside school holidays and closes some weekdays.
The Milky Way Adventure Park past Clovelly is largely indoors, which makes it north Devon's most reliable wet-weather day — rollercoasters, a train ride, pottery painting, a magic show and an outdoor falconry display people rate as the best part. Closed Mondays and Fridays.
Across the estuary and worth knowing about even in rain — there is a visitor centre with a café, clean toilets and ranger events, plus a lending library of beach toys. £8 a day, same as Westward Ho!, and you get more indoors for it. Parts of the car park flood at high tide.
The pebble ridge in a big sea. It is a huge natural bank of cobbles thrown up by longshore drift, and crossing it in weather is a proper trudge with the Atlantic doing its work behind it.
Clovelly is along the same road, and it charges — see whether you can visit Clovelly without paying.
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