York is a stunning ancient walled city with about as much history as Durham and it seems to attract many more visitors than Durham partly due to its location further south. Thankfully, York still manages to totally avoid that tacky tourist feel of some other picturesque places in the UK- it is modern, vibrant, has a huge and excellent range of restaurants/pubs/bars and is still a well preserved city.
York University is a 1960s university and, having studied there (and not always had a good time), I suggest visiting first rather than relying on carefully selected photos from a prospectus. The accommodation is not the best in the UK, some of the interiors are very 1960s, but, on the other hand, Heslington Hall (and Heslington) are beautiful, Central Hall does look striking, the huge lake is a marvel, the Computer Science building is beautiful (the department has been classed before as 2nd in the UK after Cambridge) and a huge expansion plan, starting this year with the university tecahing law for the first time, and then Film and Media and dentistry, should hopefully revitalise the university and give it the range of some other 1960s universities such as Warwick.
Still, if you want the truth of all these 4 universities, no matter how similarly they may score overall in league tables generally, Durham University still has an aura around it in quite a few people's imaginations- if you visit Durham you will get an idea why.