It's over 20 years since I last visited but some of these may be worth your time:
West Somerset Railway, steam-hauled, between Taunton and Minehead.
There's a falconry place at Allerford.
Dunkery Beacon - views in all directions including north across the coast and to south Wales and east to the Quantocks. There are usually ponies on and around the beacon.
Tarr Steps clapper bridge in the Barle valley
Lynton and Lynmouth - Valley of the Rocks and feral goats. Rack and pinion (?) cliff railway.
Watersmeet - meeting point of two rivers in wooded valleys, a few miles south of Lynmouth.
Knightshayes Court - Victorian gothic masterpiece house and gardens near Dulverton.
Dunster Castle - feudal fortress with superb views over coast and country.
Culbone Church - just inland from the coast. Said to be the smallest parish church in England and not accessible by public road.
You can also take a coastal trip on the Waverley, the last sea-going paddle steamer in the world, or get a day trip out to Lundy.