Short answer: Leechwell Garden is a free community garden with wooden climbing equipment and a sandpit — useful on 1 January with children. The Plains by the river are the flat ground.
The Plains and the quays beside the Dart. Flat, which matters here because Totnes climbs steeply everywhere else — and on 1 January nobody wants the hill.
A free community garden tucked behind the town, with wooden climbing equipment, a sandpit and a shallow stream. The answer if the party includes children with new things to try out.
Up the High Street to the castle for the view over the valley. The castle closes in winter, but the climb and the view cost nothing.
Totnes sits eight miles up the Dart at the tidal limit, so it does not take the weather the coast does. On an unpredictable 1 January that is worth something.
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 flat ground is the Plains by the river, which is also where most of the good places to eat are.
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