If I remember correctly, Tom Paxton "carefully examined every corner of the airport for the next fourteen hours or so...."

For Friday night music, it sounds like you would have time to veer off course as far as Hinckley, near Leicester. There is an acoustic session from 8.30pm, open mic from 9.30pm, at the Queen's Head. There's a bit more info at this really useful website. When the page opens, click venues > England > Leicestershire. Or email the guy who runs the website, and you'll get a quick response. (He is usually at the Queen's Head sessions himself.)

If you take up this option, you might be better taking M1 rather than A1 from Leeds. The A14 is of course a fast route to get you back on course after the music, especially at that time of night.