I have been to both Barnes Green in Grenoside, and Snowdon out towards Eckington. Snowdon had great facilities and the lessons were taught really well, however you turn up and get put on the horse, you don't get chance to handle the horse yourself. However, I don't know if I read a thread saying it had closed
I enjoyed Barnes Green, but maybe thats because I had such a good RI! There is only an outdoor school which is annoying when it rained as you could only use half the school! We did do quite a bit of jumping, and beginners dressage training, but the school is too small to do a course of jumps.
Sorry I haven't been able to recommend anywhere, but I hope my opinions helped!!