If you descide on the A59 here are a couple of little pointers to make it easier.
When coming down the hill to Harrogate just outside Harrogate you will come to a roundabout, turn left on to the B6161 to Killinghall, (it joins the A61 after a couple of miles & cuts the corner off).
Then when you get to the final roundabout on the Ripon by pass, you will see a small road to the right signposted Sharrow, take this & it eventually goes under the A1M then round a couple of small roundabouts & then down the slip road onto the A166 /A19.
(There is a Littl Chef not far down the road for a comfort break)
Turn off the A19 at the A172, if you cut the corner off by going on the A173 through Gt Ayton just before you rejoin th A173 you will pass a car park for walks to Rosebury Topping, there is a loo in the car park ( I can usually make it to there in one go but not Whitby)!!!
Then A171 all the way to the promised land.
Enjoy yourself however you get there.
Cheers
Les