I'm a new member here and I'm from Leeds so I thought I would contribute to this thread; I hope you don't mind.
The main nights in Leeds, or should I say the busiest, tend to be Mondays (Queens Court £1 a drink night, and then Mission aka Homo £1.50 a drink) or Thursdays (Queens Court £1 a drink night).
I would say that they seemingly attract a younger, more student-esque crowd however...and so may not be of taste to your friend.
I, personally, enjoy Wednesday nights for 'Rock and Roll Bingo' at QC...followed by Kareoke at The New Penny...tends to be a varied crowd and a good chance to win some pennies.
On a weekend The New Penny is very diverse and tends to attract a mixed crowd, mostly more mature people...and the same can be said for the likes of The Via Duct, The Bridge and The New Penny.
I'm up for making new friends, so if there is a night out....please keep me posted.
I hope this helps =)