A few years ago I was on holiday in this area and whilst walking through the old part of town, came across a lovely wholefood shop which did B&B, so we booked a couple of nights there. There was a fantastic restaurant virtually next door for our evening meal & breakfast and the food served up was absolutely stunning - very high class veggie. The rooms were beautiful, not very expensive, and I would happily return there. Here's the link
http://www.whitbyonline.co.uk/business/singles /shepherdspurse/