I live near Yarm, and am thinking of moving to a place just off the High Street. It's a lovely market town, with a high street that's consistently voted one of the best in the U.K. Lots of good independent shops, rather than th usual identikit names, and plenty of cafes and restaurants. Yes, parking can be a pain sometimes, but it's such a minor disadvantage, and you get to know how to get round it.
It has a fantastic quality of life for families - loads of places to go and things to do. Transport links are good, it's easy to get around - the A1 and A19 are handy, and the east coast mainline is close by at Darlington. Yarm has two stations, which link to Darlington and to Manchester Airport. Within half an hour's drive you have the coast, the North Yorkshire Moors and the Dales, and it's easy to get to Newcastle and Leeds as well. There's Conyers School, and also Yarm School, an independent which goes from nursery to sixth-form and is very well-regarded.
Yarm itself isn't rural, but the rural isn't far away, so you really do get the best of all worlds.
Oh, and the best day out is Great Ayton, about ten miles from Yarm. Birthplace of Captain Cook, you can climb up the hill to his monument and then back to Great Ayton to Suggitts, an old-fashioned sweet shop who make the world's best ice cream, and a paddle in the stream.