A very Brief trip into York found these two Shops. There is a Virgin and HWV in the centre of the shopping area and other record shops around town. I had about half an hour and uncovered 2.
The best vinyl shop in York (Depth Charge) used to be on Gillygate but that closed its doors about 10 years ago.
Track records on Goodramgate is not too bad, vinyls upstairs and cds downstairs (i've not been to it in a few months)
EQ is a little shop hidden away down stonegate arcade, it sells clothes but also has a little vinyl selection, mostly 2nd hand.
There used to be wildcat records on Micklegate but i'm not too sure if its still there, i think it merged with another shop and is now selling classical music only.
There are very few music shops in York nowadays, i prefer vinyl shopping in Leeds - a 30 minute drive away