| have to agree with everyone about the guided C2C routes - they've been designed with an eye to gentle off road routes, away from traffic. My commute crosses the Walney to Wear route, which would be awful on anything other than a MTB with decent fat tyres, since it includes Sleightholme Moor, Hamsterley Forest Drive and lots of rough farm track. Pleasant in its own way, but useless for eating up the miles.
Back OT: If you're fixed on Whitby, I'd suggest taking the A174 (Coast Road) to get there. The A171 is a fast, dangerous road, and the Eskdale route is hillier and longer. The A174 serves as a good compromise, provided you join it somewhere after Eston - and preferably after Saltburn. Before Eston, it's virtually a motorway, and the local yoofs race along it at x mph.
For the rest of the route, it depends on how much climbing you want to do
It's a shame the A66 is unrideable.
I was planning an incredibly stupid route going over the Lakeland passes, Hartside, Killhope Cross and (probably) Crawleyside, before heading through Durham and finishing at Hartlepool. But my girlfriend does live in Poolie, so I have a good excuse for going there.