Great choice - I was at uni there for three years and miss the place like mad.
Having been there as a student, I'm best placed to recommend places to drink
The House of Trembling Madness is a really interesting place to go for a drink. If you want to get silly drunk, go for a Shed 7 at Evil Eye (costs a tenner, but you won't need much more for a while afterwards!) There are some decent places along the river - quite a range too. Revs is decent in the day with a big-ish outdoor bit if the weather is nice, and the same for Pitcher & Piano. But if you want cheap treble vodkas, you're looking at Lowther or Stone Roses (great place). Micklegate has a load of places too.
In terms of food, Kennedy's used to be really nice. I think they changed the menu up a few times and it's been a wile since I was around, but it never let me down at the time.
Classic York things to see would be The Shambles, Stonegate, the Minster, the Castle, Clifford's Tower, Jorvik (Viking) Centre, York Dungeons... etc etc
Hope this helps. If it doesn't, I'm happy for the excuse to take a trip down memory lane anyway!