Short answer: Sunday works well in Plymouth. The Box is open — it is Mondays it closes — and so is the aquarium, which shuts Wednesdays. The catch is eating: the Barbican Kitchen and Tio Leo are both closed on Sundays, so book somewhere that is not.
Both of the big indoor attractions are open on a Sunday, which is not true of every day of the week here. The Box closes Mondays. The National Marine Aquarium closes Wednesdays. Sunday clashes with neither, which makes it one of the better days to visit.
The Village Restaurant does a good-value set lunch and specialises in seafood; book, and expect it to be loud. Fig & Thyme is the Barbican brunch option, best early. Pier One opens at 7am every day with a log burner and sea views and is popular with dog walkers, which makes it the reliable Sunday fallback.
The Hoe, the Barbican, the Mayflower Steps and Royal William Yard are all unaffected by the day of the week. Devil's Point still gives three hours of free parking. A Sunday in Plymouth can cost nothing but lunch.
Hoe in the morning for the view, the Box late morning while it is quiet, lunch on the Barbican somewhere booked, then the walk west along the water to Royal William Yard and Devil's Point. That uses the one day of the week when neither indoor attraction is shut.
Both the Box and the aquarium are entirely indoors and both are open on a Sunday. That is a better wet-weather position than almost anywhere else in Devon, and it is the reason a Plymouth Sunday survives a forecast that would ruin a coastal one.
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