There is a brilliant Cinema in the centre of town called City Screen which plays all the usual stuff but also plays independent films, has a lovely bar and gigs etc. on downstairs:
http://www.picturehouses.co.uk/cinema/York_Picturehouse/ There's also a VUE (I think) cinema at Clifton Moor which isn't too far out of York, but you'd have to get the bus.
As for life there, it's a really lovely city and everything is in walking distance which I really liked and miss now I'm in Manchester (although I think it's a bit of a walk from the uni into town, maybe half an hour, but there are lots of buses). As you may have read already, it is not great for clubs. There are one or two big ones that I never went in (The Gallery and Tru) because they weren't my kind of thing, and then The Duchess and Fibbers which are much smaller but play a more interesting range of music (kind of - it's worth a Google to get an idea). If you like 'old man' type traditional pubs it's absolutely brilliant, and also has places like Vodka Revs if that's your thing. There are nice independent shops, as well as the usual places like Topshop and Newlook.
After 6 years there, my boyfriend and I wanted a change because it can get a bit small. You'll find that you see the same faces again and again, and your nights out won't vary much! I don't think that'd be a problem for 3 years though and it's still big enough to find some variety. Oh and tourists are another downside, it's always really busy on a weekend!
So to conclude! If you want a huge city where you can get lost, go to a different club every night of the week etc. then York probably wouldn't suit. But if you're looking for somewhere friendly and fun, with a bit of history, that isn't too intimidating but that isn't like living in a tiny town it's definitely worth looking at.
I hope that helps a bit - if you have any questions just let me know. On a more sensible note, I know quite a few people who went to York uni and they are all highly intelligent, interesting people who are doing well for themselves. I think it gives you a really good start in whatever you want to do