Get the ferry from Padstow harbour over to Rock. It's a lovely dog friendly beach to the left with the dunes called Daymer Bay. Going right is Rock, not that's there's much there. But there is a lovely cafe called Blue Tomato there which welcomes dogs ( and just a few shops but generally dogs wait outside those) It does breakfast and lunch and some evenings dinner, but you need to check and check the ferry times too. I believe there is also a night ferry taxi. There is also a pub type restaurant by the seafront on there called the Rock Inn. We have previously taken 2 dogs for a big group booking and sat on the balcony, but I don't know if you can generally.
Padstow as others have said most places pubs/ cafes let you have dogs in there outside seating, which is pretty limited.
You can drive into Weybridge and there is an American Diner called Route 39, which allow dogs in their orangery / conservatory bit to eat. There are loads of other restaurants/ pubs there depends on what you like to eat. The diner might be a hit with the DC?
Cracking crab ( sea food) I believe you can take dogs (do check all these though I now own a 3 year old and despite going every year to Rock opposite Padstow I haven't been out so much to eat in the last few.) The cracking Crab is in Polzeath up from the surf beach, but you can't take dogs on that beach in summer season so would be better for an evening meal and wonder around before / after as is a fair drive around from Padstow.
There is a lovely beach quite quite along from Padstow called Harbour cove. It's a reasonable walk from the parking so nice for dogs, but nothing there facilities wise. It's opposite Daymer Bay on the Padstow side of the estuary. It allows dogs all year. So take a picnic !
I've found most pubs allow dogs in the bar areas indoors to eat, but not in the restaurant. Always worth asking etc.
You can even take Dogs to the Eden project, but not inside the Domes. So we have done it by splitting up ( pre-Dc) It's ok if nice weather to eat outside or picnic, but you can't take them inside the restaurants.