Any walking countryside area usually allows dogs in most shops and pubs if you ask first. Most realise their owners are going to spend money!
A lot of National Trust places have land, woods, walkies alongside the historical houses and parks there are some places we head for as they are better motorway stops when travelling on hols etc. If you are a member you can park for free, walk the dog and have a cream tea in a lovely setting.
Having said that all motorway service stations offer dog walks, toilet areas (occasionally concrete dog loos) water bowls and some offer free food / snacks for your mutt too. Some of the walks might be a bit naff at motorway service stations but we travel extensively and have fav stops all over the country. it is vital you train your dog to go to the loo on command whatever the patch of land or concrete dog loo you are offered makes travelling easier.
Some tourist sites allow dogs into certain areas check on their websites or ring them and ask. We avoid places that say no to dogs in outdoor areas or that offer wire 'kennels' to park your dog. Some shooting area pubs / accomodation offer kennels overnight yuk.
Majority of Scottish and irish ferries have dog allowed areas on board. Some expect or allow dogs to stay in vehicles others allow them on certain decks. Our dog has her sea legs.
Many dog friendly pubs, hotels, b&bs allow dogs in certain areas separate from any restaurant in case non doggy people complain ignore the hygiene excuses they allow guide dogs in by law so it is used just as an excuse to avoid confrontations with bad dog owners. Like kids some people haven't socialised their dogs to behave in public! Some have dog and non dog bedrooms in case any customers have allergies as well.
We have stayed and dined in some fab pubs that are dog friendly especially in Cumbria, the Lake District, Cotswolds, cornwall, wales and Scotland. Posher hotels will even offer dog sitting and dog walking for customers. There is a lovely cafe on snowdon that allows dogs in too and dogs can travel on many of the steam railways around the area.