We walked the 7 mile Robin Hood Bay - Whitby section in late February. It's a pleasant walk, though it might be a little more interesting to follow the Cumberland Walk out of Robin Hood Bay as that path is right on the cliff tops. The path was in pretty good condition throughout and I would say it was suitable for all Bicycles and not just mountain bikes. We parked for free in Robin Hood Bay (theres a charge March to October though) and then we got a bus back from Whitby in the evening which was £3.80 each.
The best part of the walk was looking around Whitby at the end. It's a really picturesque little town with loads of loads of little cafes and gift shops etc. Even during a rather cold winters day, the little streets were very busy with visitors, so it may get crowded during Summer.
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