Well, it's according to taste. The Magpie is, of course very well-known and I can vouch for the quality - but you'll be lucky to get in without booking. It's great. However, I've had equally brilliant F&C in several other places in Whitby - several pubs on the quayside for a start.
For a general recommendation I would say consider the Hare and Hounds at High Hawsker (couple of miles S. of Whitby, but convenient for the Abbey. I have always had excellent food there, but I haven't tried their F&C. Have fun trying. :)