I'd recommend the York Museum & Gardens. The art gallery is good (&free) if that's your thing. Jorvik is looking a bit dog eared now, and is expensive for what it is. There's usually a good queue for it too.
It's also definately worth a walk around the walls. Yuo get some good views of the city. There are plenty of coffee shops of the Starbucks/Nero/Costa type, but lots of little indepemdent ones which are on the whole far nicer. Avoid Betty's unless you like taking out a second mortgage for tea and a cake (and 15minutes queueing outside while elderly folk chew their scones and watch you from within without pity.)
The Railway museum is outstanding, even if you have no interest in 'spotting'
http://www.nrm.org.uk/ . If the weather's good, you can cycle the solar system
http://www.solar.york.ac.uk/ which seems to be getting very good reviews.
The evening/night life is good, with a wide variety of pleasant ale houses and nightclubs, and an abundance of good resaurants. I'd personally recommend Loch Fyne and The Blue Bicycle, both on the Foss Way Bridge in the city centre.
York isn't car friendly. If you're driving in, either use the excellent park & ride or leave the car at your base and hoof it around the city. Everything's within walking distance apart from the outlying retail parks on the ring road (better not let the significant other know about those).
Plus in a pinch, the local dealer, JCT600 VW York gets a good review from my friend, and he's a bit picky.
Hope you enjoy it!