Gregory's on Bishopthorpe Road, York is a small guest house in which I stayed for 2 nights in March. It has, I believe, only 4 rooms and is run by a friendly couple. One reason I chose it was because it was walking distance from the city centre (I was in York for a conference at the Barbican).
I especially recommend breakfast - this is the only hotel in which I've stayed where the bread is baked and the jam is made by the proprietor. Worth a stay.