John, if you can afford it, and can be in Whitby all week, a pass is the best bet; you can go in and out of gigs as you choose, so if, for instance you want to see just one performer at one venue, then move on to another, you'll be able to do that (subject to there being seats available). On the other hand, if you're wanting to meet up with mudcatters, can't be in Whitby all week, or want to enjoy lots of free live music, spend your time in the pubs listening to sessions and singarounds.
You'll find a list of events posted up in the Tap and Spile, and can buy a programme there.
Whichever is the case, get yourself along to Whitby; you'll not regret it1