Mark,
There is so much to do in York it is difficult to know were to start.
There are excellent museums, galleries, the Jorvig Centre, National Railway Museum( we usually spend the whole day there), York Minster ( not just to view but have some good concerts, the old streets of York such as the Shambles, good walk round the City wall, ferry trips on the river, a good theatre.
The real must on every visit for us is a visit to Betty's Tea Rooms. We prefer Little Betty's Tea Rooms in the Shambles, it is like going back in time with excellent food and service.
York is dog friendly. Check the web site " dog friendly pubs.co.uk".
As well as the tea rooms there are some good restaurants,cannot recomend one as we always eat at Bettty's Tea Rooms.
Hamer