Hello, I used to live in Ilfracombe (about 14 miles from Barnstaple) so have know the place like the back of my hand!
Beaches - you are spoilt for choice. Woolacombe, Croyde and Saunton are all within 30 mins drive and are beautiful. They are really gorgeous beaches. Croyde is very surfy (watch the undertow with your little ones), Saunton is a very long, wide beach which doesn't get as busy as the other two, and Woolacombe is the busiest of the lot, there are rides on the beach, plenty of shops and ice cream places. These are all sandy beaches but there is a pebbly beach called Barricane next to Woolacombe main beach, which is great fun for rock pools etc.
Woolacombe has also got plenty of seaside shops, pitch and putt, crazy golf, all the rest.
There are also plenty of places to go with your kids, some (frankly bizarre) theme parks. The ones I would go to are The Milky Way (you can feed lambs, watch falconry, there is a bid indoor and putdoor play area), Watermouth Castle, Exmoor Zoo, The Big Sheep, Combe Martin Wildlife Park - all of these are within 40 mins drive. I think they have all got websites.
What else would you like to know?