Snow Hill, have a look at The National Railway Museum. It's really interesting and best of all, it's free! #yorkshire. I also recommend the McArthur Glen outlet. As Grapau says, there's lots of shops and the parking is free and there's plenty of parking spaces. If you've time, a trip to Harrogate is highly recommended. It's a really nice town. Fountains Abbey is about 1 hours drive from York and is again well worth a visit. Its not cheap though. Its £19 for an adult. The Royal Armouries in Leeds is about 40 mins from York Centre. It's brilliant and best of all again, it's free!!. Have a great time wherever you decide to go.
Janine