University of Manchester
The Observatory holds weekly meetings, and anyone can stop in as a guest for the chance to see some truly spectacular sights through the impressive double telescope. That being said, if the weather's being its usual British self, the view of the city from the roof of the Sackville Street Building is pretty awe-inspiring in its own right.
See a lunchtime concert at Chetham's
One of the country's top schools for music, Chetham's likes to spread the love by showcasing some of its rising stars with a free lunchtime concert series held at Carole Nash Hall. The shows run from 1:30pm to 2:10pm on Tuesdays, Wednesdays, and Thursdays (while school's in session), and there's no booking required: all you have to do is show up. You should probably call ahead to make sure the concert's still on, though, just in case.