About 50 miles from York is the seaport of Whitby. On the first weekend 29/30 of April 1/2 May (which is a bank-holiday weekend in the UK) there is a folk festival based in the town. If you find froots on the google search engine you will find a list of festivals by date which in turn will give you a link to the festival web-site. Furthermore look up Tykes News and Filofolk for details of clubs and pubs in Yorkshire with folk music sessions, there are quite a few to go at

Cheers

Raggytash