Culture vultures
Manchester Art Gallery
Has over 25,000 permanent exhibits for a serious, big-time history hit. Oh, and you'll need a sit down afterwards.
Cornerhouse
Is a thoroughly modern must-see for contemporary arts, book and independent film fans (and they do a nice sandwich too).
Urbis
Is an uber-hip exhibition centre. You could just stand outside and go 'Wow!' but it's worth checking what's going on inside too.
Manchester Cathedral
Gives you that kind of humble feeling you only get when you're looking at over 1000 years of spiritual history.