Don't know about Exeter and Birmingham (though I imagine Birmingham being a major city would have top notch clubs).
York's nightclubs are surprisingly good. There are 3 or 4 major ones (Tokyo, Salvation etc) and a few smaller ones which really should be lumped into the bar category, such as Vodka Revs and so on.
There's a student night for a given club every night of the week so you can go out whenever you feel like it.
The bouncers are sub-standard, unintelligible faggots with very poor manners, but what's different?