Dulverton is at the foot of Exmoor National Park. Some fun facts about Exmoor: it is the highest coastline on the British mainland, home to rare species like the Exmoor ponies and red deer and one of Europe's Dark Skies Reserves, perfect for stargazing. https://www.visit-exmoor.co.uk/things-to-do-around-exmoor This article from the Guardian highlights great day trips, experiences while you are in Exmoor. Get your hiking shoes and explore some of the beautiful hikes!
Amazing pub/restaurant with great wine list and local food. Reservations are probably necessary.
Founded in 1895, the National Trust is a conservation charity protecting and maintaining historic places and natural beauty for public benefit. There are plenty of beautiful National Trust sites close to Dulverton to explore!