In Dorset there's Lyme Regis and Swanage. Both have nice sandy beaches with shallow water bays, great for the kids and as safe as you can get when it comes to sea bathing.
I had quite a few holidays with my kids at those places and they never got bored, although there's little in the way of theme parks or fairground rides.
Dunno about Devon and Cornwall as regards kids, but Watergate Bay in Cornwall must be one of the best Sandy beaches ever and it's great for surfing. It's near Newquay. I love Polperro as well, but no beach to speak of.
In Devon Dawlish and Dawlish Warren are quite good for kids as I remember, but I'm talking a long long time ago (when I was a kid) so can't remember too clearly.