The number of people educated at private schools is higher than some places, but I've not many people who I'd particularly call a snob (well... mentioning no names, certain societies attract them). There are just as many arrogant/stuck up people as there are anywhere else, from all school backgrounds.
The nightlife... endless threads on this. It's fine, it's more than bearable, a lot of people really like the strange nightlife we have here. Leeds is only 35 minutes and £6 on the train, no big deal.