The Graph's Gaff is in Aycliffe Village, on the edge of Newton Aycliffe. It's handy for the A1 if you're driving up from the south. The village itself is old, with a green and a proper pub next door.
It sleeps six, with three bedrooms. One has a kingsize bed and an en-suite shower room. The other two are twins. There's a family bathroom as well. It's got a 4 Star rating. It's roomy and clean, with a decent kitchen and a separate dining room.
You've got the pub literally next door. They do food and have events on sometimes. There's a hotel on the green that does good meals too. The River Skerne is a short walk away, and you can follow it for a proper country stroll.
Darlington is about ten minutes by car. It's got all the shops you'd need, and the train station is good for getting to York, Durham or Newcastle in under an hour. The Railway Museum there is worth a look if you're interested in that sort of thing.
Within half an hour's drive you can get to Durham city. The cathedral and castle are great, and the river walks are nice. Beamish Museum is about 25 minutes away, and it's a good day out if you've got kids. For a walk, High Force waterfall up in Teesdale is about 45 minutes, but it's impressive.
Facilities are all there: WiFi, Smart TV, washing machine, parking. Bedding and towels are included. The garden is yours to use. Sorry, no pets.
Some links if you're planning trips out: Beamish Museum, Durham Heritage Coast, and North York Moors National Park.