Like @gogohmm, I am reluctant to reveal the hidden gems of Somerset and just over the border into North Devon, but, since you twisted my arm...
All along the Bristol Channel are some stunning secret places although, caveat, none have sandy beaches except Dunster and Minehead. Kilve, Donniford, Quantoxhead and St Audries Bay brilliant for fossil hunting, Watchet has a gorgeous harbour and, during the summer holiday period, the Town Council put on many free activities for children. Further along is Blue Anchor Bay with free parking all along the sea wall. Beyond Minehead the A39 coast road takes you to Porlock and then across the fringes of Exmoor where you will see the wild exmoor ponies grazing, the hauntingly beautiful Doone Valley and beautiful views across the Channel to Wales. And, at night, when the moon is rising and shining across the Channel, it always brings to mind the song ' Moon River' from 'Breakfast At Tiffanys'. From Porlock you next reach Lynmouth/Lynton with the amazing furnicular railway and, just outside Lynton, the Valley Of The Rocks - a very special, tranquil and beautiful hidden valley with, allegedly, the highest sea cliffs in the UK. The true story of the 'Overland Launch' starts at Lynmouth and, if you follow its route back to Porlock and the descent down Porlock Hill, it is a mindblowing tale of human endeavour and selfless heroism.
Now I have given it all away, but, being fortunate enough to live nearby, it would be selfish to not share it!