Actually, if you've never been to York, you're missing a treat. The museums are amazing and walking the walls of the Minster would be a great adventure for an 8 year old. I went when I was a 9 year old girl and I've never forgotten it. Also, you don't have to stay in York itself, which can be pricey. Find a B+B in one of the outlying villages and drive, or bus into York.
If you like walking and good views, it's worth a look at Hope, or it's surrounding area. It's even lovely in bad weather, but you'd need transport.