Whatever your particular interests, for an overview of all that Exmoor has to offer, you will find more at https://www.visit-exmoor.co.uk. The nearby Quantock Hills AONB area is also described here.
Exmoor is a National Park. https://www.exmoor-nationalpark.gov.uk
Wheddon Cross is the nearest village approx 3 miles away. The village is said to be the highest on Exmoor, standing at 980 feet above sea level. The highest point on Exmoor, Dunkery Beacon (1704 feet above sea level) is only a short distance beyond. There are fantastic panoramic views from Dunkery; wild moorland to the west, the Bristol Channel and Wales to the north, the rolling Brendon Hills to the east and the Quarme Valley to the south. Some of the best walking on Exmoor (including a trail suitable for those less able) can be found at Webbers Post which lies to the seaward side of Dunkery Beacon.
For the active visitor, walks with fine views are all around, whilst Exmoor's well-known landmarks such as the outstanding Tarr Steps, can be reached by driving across the moorland area which can be seen from West Huckham Barn. Dunkery Beacon, and the valleys of the Exe, Barle and East Lyn (setting for Blackmore's famous novel Lorna Doone) are all easily reached. Wimbleball lake, with a wide range of water and land based activities, is within easy reach. (5 miles) Excellent walks and cafe with outdoor eating area. There is ample information available at the barn to help you in planning your visit.
The medieval village of Dunster is only six miles away, with its 11th century castle, and Mill (National Trust), and old Yarn Market, Tithe barn and interesting shops, pubs and restaurants.
Slightly further afield is the North Devon and Somerset coast with pretty villages in steep combes such as Porlock, Lynton and Lynmouth. For a more traditional seaside experience, you can head to Minehead which is only ten miles away.
Other towns to visit in the area are Tiverton to the south, with plenty of shops, a canal walk, and a National Trust property (Knightshayes) nearby. A visit to the county town of Taunton, to the north, could be combined with a day exploring the beautiful and little-known Quantock Hills.