If you are staying in Minehead then I would recommend walking a section of the South West Coast Path.

The South West Coast Path is easily accessible from Minehead beach. The first section is grassy and you can get good views of the sea. The next section was quite sheltered as the path goes in a wooded area and there is quite an incline, nevertheless you can see the sea through the trees. There was a point where the path split and we took the lower road, which takes you through a massive field and down to a very pebbly beach. There aren't any shops or pubs along the way so it would be sensible to take some food and drink.