The city walls surrounding York, are the key aspect of the city. They surround most parts of the city, with the exception of certain areas (such as Bootham) which were demolished at points. The walls have various access points called 'Bars' - Micklegate Bar, Victoria Bar, Walmgate Bar, Bootham Bar, Monk Bar (Think thats all of them!). In Monk Bar, you have got a museum, dedicated to Charles the 3rd, who was held in prison in there. From pretty much all points of the walls as you walk round, there are spectacular views of the city - The Minster, The Yorkshire Wheel, and Cliffords Tower.
Best things to see in York are the Minster, National Railway Museum, Jorvik Viking Centre and the City Walls. Plus check out the ghost tours which are great fun. take a look at www.holidayinyork.com Its also a great place to live - not too big, but its got everything you need; and Leeds & Manchester are not far away. I would definitely recommend a trip to York!