We stayed at the "Lynton Cottage Hotel" and were very pleased; it's a child friendly place and the view from our room (C.S Lewis Suite) was breathtaking. The Victorian Cliff Railway is a touristic attraction but it came very handy to go down to Lynmouth, especially with buggy. It's a nice walk from the hotel but it's quite steep and therefore very tiring with a baby.
The Valley of Rocks is just beautiful. Wen went hiking there every morning. At some points it's very narrow but it was easy to go with buggy. It was usually only us and goats in early mornings.
The only thing that made me miss London was food. We had breakfasts at the hotel and then for lunch and dinners we tried different restaurants and unfortunately I have to say that all the places that we've tried were bad. Really bad. I'd expect some great sea food but nothing was near "good". Hope there'll be improvement food wise, because we're definitely planning to go there again!