The Lakes lots to do if you like walking, trip on the Gondola (Coniston) and see Ruskin house( very interesting) great cafe nearby.
Arts and Crafts house at Windermere. Trip on the boat from Windermere to Ambleside then have a wander, a drink at the hotel on the jetty and back on the steamer. Grasmere. Ullswater and walk up Hallin Fell a good one if you are a beginner and fantastic views from the top.
The Scilly Isles Tresco gardens very unusual.
Jersey lots to do and you can hop on and off the bus. Busy in St. Helier but quiet in other areas. The tunnels are fascinating.The Crab Shack if you like seafood. Unusual church nearby.
The Jersey Pottery
Northumbria -Holy Island, Bamburgh lovely restaurants and the castle. Alnwick- gardens and some of Harry Potter filmed there.
Beamish
Airbnb with a cosy fire in the evenings.
Yorkshire- Dales, Hawes, Askrigg All creatures Great and Small filmed here lovely little village great pub. Steam train at Pickering to Grosmont ? Sebergh - Farfield Mill
I would look for a cosy Airbnb if you want to be on your own. Walk in the day, fire at night, good local produce and a great book or two.
Lots of people go to these places on their own, you can speak to people walking if you feel like it or not.
Hope you enjoy it.