Short answer: Dartmouth Castle has indoor sections and a tea room, and the ferry ride out to it is good in rough weather. Across the river, the Dartmouth Steam Railway runs whatever the weather. For sitting it out, Café Alf Resco has a covered courtyard and Dudley's has an extensive gluten-free menu.
It has a castle, a steam railway, narrow Tudor streets to shelter in and more good places to eat per square mile than anywhere else on this coast. The river is dramatic rather than spoiled when the weather turns, and the boats keep running.
Part medieval and part Victorian fort at the mouth of the Dart, with a gun battery dating to the 1300s and St Petrox church alongside. There are indoor sections and a tea room, and the approach by boat from town is more fun in a bit of weather than in flat calm. Be aware there are a lot of steps — not suitable for pushchairs or wheelchairs.
The Dartmouth Steam Railway runs from Kingswear, a short ferry hop across the river, and a covered carriage is a genuinely good place to be in the rain. It is one of three steam lines in Devon and the most convenient one to reach without a car.
Café Alf Resco is the Dartmouth institution — open from seven, with a covered courtyard, excellent brunch, strong vegan options and a famously dog-friendly welcome. It is small and it queues, which is the price of it being that good.
Dudley's on Lower Street has one of the best gluten-free menus on this coast — a full separate range rather than a token option — plus crab sandwiches. Closed Wednesdays. The Cherub Inn, the oldest building in Dartmouth, is the most characterful room in town but has about seven tables, so arrive early.
Do not drive out to the coves in the rain. Sugary and Compass are down steep steps with no facilities, and Compass involves a long flight of wooden stairs that gets slippery. Save them for a dry afternoon.
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