Hello,
I've lived in York for about 12 years. My husband, daughter and I live near Bishopthorpe Road and we are very happy here. Obviously, it is not as big and cosmopolitan as London but it has lots of attractions.
Just up the road from us is a parade of mostly independent shops: a deli, green grocers, a lovely cafe called the Pig and Pastry, a nice sandwich/cake shop, a brilliant hardware shop (it seems tiny and yet seems to have everything from step ladders and nails to sledges and irons!), a Thai restaurant, an excellent butcher. It is lovely to be able to pop up the road for almost everything we might need.
In the other direction is Rowntree Park. It has a lake, tennis courts, playgrounds, gardens, a little woodland walk, and a lovely cafe that is part of the central library so you can borrow and return books there too. We are also close to the river and the racecourse which are both nice for walks, jogging and cycle rides.
We are a 10-minute walk from town. The city centre isn't huge but it is beautiful. There are good independent places to eat and lots of little shops, as well as the more obvious chains. The Minster is beautiful and the centre is lovely just for a wander around. There are various museums, theatres, and a newly refurbished art gallery.
There are good places to visit not far from York, if you drive or can hire a car for a day. Beningborough Hall is a National Trust property with gardens and an adventure playground. Other historic houses not too far away are Castle Howard and Newby Hall. A trip to the coast for a day is also manageable if you drive; Bridlington is about an hour and a half away. Scarborough can be reached by train. Whitby/Sandsend is a little further but worth a visit. There is also Dalby Forest, managed by the Forestry Commission, with playgrounds and cycle paths. Leeds is easy to get to by train or car and has lots of shops, although it isn't as nice to potter around as York.
The city has become popular with groups of drinkers at the weekend. I am sure this is not unique to York but is perhaps more obvious because the centre is small and because it seems incongruous against such a pretty backdrop. It doesn't bother us too much as we don't go out in the evening all that much; our daughter is 6 and we eat early if we go into town. Sometimes we have been approached by groups of people who are plastered before 7 pm but usually it is to ask directions to the all-you-can-eat buffet!
I hope that gives you a starting point. You can catch a train direct from Kings Cross into York and could just about manage a day trip if you set off early and go home late. It takes just over 2 hours, depending on which train you catch. You could come and see York for yourself.