Taken the dogs I walk to Cannon Hall. It's very dog friendly, but as you say has the space. If I go in a pub with the dogs (currently looking after 3, as their owners are away), I always try & go somewhere with plenty of space. They are well behaved dogs & most people like them a lot, but obviously some folks are scared / allergic / just don't like them, so I try to avoid smaller places as a rule.
The George In Bridlington is very dog friendly, doesn't serve food but they always bring snap art n water for any dogs that are in there.