Route from Newark to Flixton near Filey

We are driving from Newark to Flixton tomorrow, probably taking the longer route which goes up the A1 then across on the A64. The alternative route (A15, Humber Bridge etc would mean taking the Driffield /Foxholes Rd which I gather is not the best for towing.

Any tips for decent stopping place on the A1/ A64 route please? 

Plus any tips for the Cleveland Way ( with regard to walking/ car parking for walking and cafes) running along this section of the coast would be interesting.

Thank you!