I used to work at Naburn Grange in Naburn (between York and Selby), which was nice when I was there (approx 1999/2000) but no sure what it's like now.
I have also had some lessons at Oxmardyke EC ( http://www.oxmardyke-equestrian-centre.co.uk/) , which had lovely facilities and nice horses, although the instructor was a little chatty to the regulars and yard girls, but aren't they all.
Oh yes I've ridden at Jodphurs too, but it's the wrong side of York for what OP wanted. I used to be taught by Maggie, owner of stables, I believe, who was lovely. They too have a website I believe.... ah yes... http://www.jodhpursridingschool.com/
I used to go to a fab one near Wiggington, Moorhouse RS run by Mrs Kemp-Welsh, but I think it has since closed down.
Oh found Naburn's website too... http://www.adveb.co.uk/naburn/
Have also ridden at Bleach Farm in Stamford Bridge but that was years and years ago and not sure if they still do lessons.
Yep ridden at Oxmardyke a year or so ago - might go their again. Was very nice, rode a very nice horse called Davey. I live over that way at the mo but am looking to move towards York / Selby so looking more in that direction. Did phone Naburn this afternoon for prices.
Was really just nosey as to where everyone else recommended - wondered if I was missing somewhere!
The Yorkshire Riding Centre, near Harrogate - Chris Bartle's place. May not be quite the right area, but well worth travelling to, good facilities, excellent instructors, and if you're lucky the German eventing team!