The sessions in Whitby are many and varied. For instance last year there were workshops (normally mid morning) on Whistle, Melodian, Concertina, Fiddle and Ukelele. Past years have seen other instruments, Guitar, banjo, Bodhran etc etc.
Last year the organised music sessions (as opposed to the fringe) where held in the Middle Earth, Fisherman's Rowing Club, Dolphin, and Conservative Club.
In addition to the festival "proper" there is a huge fringe element at Whitby which can normally only be found by wandering round and listening out for the music.
You're sure to find something that ticks the box during the week. Good Luck!