Short answer: Ilfracombe Aquarium on the quay and Ilfracombe Museum near the seafront both work in the rain and are within a few minutes of each other. Watermouth Castle, ten minutes east, has enough indoors to fill a wet day with under-tens. The harbour is worth walking in bad weather anyway.
Of everywhere on this stretch of coast, Ilfracombe is the one that copes. It is a proper town with a museum, an aquarium, a theatre and a high street rather than a beach village with a car park, which means a wet day here has actual options rather than a long lunch and a drive.
Right on the quay, laid out as a journey from moorland stream down to open sea with every species native to Britain. It is genuinely small — some visitors are through in twenty minutes — but the staff are what make it, and people who linger report spending two hours because someone showed them the crabs and starfish feeding. Closed Fridays. Parking directly outside.
A cheerfully overstuffed Victorian collection near the seafront — local history, taxidermy, film of the old Barnstaple railway line, and enough oddities that children with a scavenger-hunt sheet stay interested. Closed Mondays and Sundays, which catches people out.
Watermouth Castle is the bigger commitment and the better bet with young children. Walk-through castle rooms, dungeon scenes, a gnome village, arcade machines, a maze and a toboggan run. Enough of it is under cover to survive a wet day, and it is squarely aimed at the age group that gets most miserable in rain.
Do not write off going outside. Verity on the pier, the boats, the walk up to the chapel on the hill above — the harbour is the most-reviewed thing in Ilfracombe and it is dramatic rather than ruined when the sea is up. Then eat: the Lime Kiln has the best sit-down view in town, and Annie and the Flint at the top of the high street does the best coffee.
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