Inn on the Shore - Downderry. A nice easy stroll along the beach from Seaton. Dogs are allowed in the bar and outside, but not in the restaurant. You can eat in the bar, but best to reserve a table if the weather is iffy, as there are only 3 tables.
This is The Hidden Hut, Porthcurnick Beach near Portscatho. They serve delicious lunches and also hold Feast Nights throughout the season from April to October, which are very sociable and great fun - and the food is great too, all cooked outdoors over charcoal in massive pans. Tickets for these sell out the same day they're put on sale, so join the mailing list to get advance warning of the ticket release date. (Then pray for good weather on the night of your Feast!) Friendly dogs welcome.