I spent a few days there about 10 years ago and enjoyed the history of the place - Yorvik (the Viking exhibition) is great, as was the Railway Museum, York Minster and the various ruins dotted around the city walls. Enjoyed a river cruise too.
I do remember that the city "closed down" at 5.30 - 6pm, very little to do (other than restaurant/pub) - no late night shopping for instance - but it was 10 years ago so maybe it's changed.