Just to echo what's already been said since I lived with several archeology students in my first year. The walk to Kings Manor is quite easy (by my standards anyway) but lots of York students cycle too, and there's bus connections. You can always look for housing nearer the city centre for your 2nd and 3rd year, but in my experience the social/college aspect uni accommodation provides is valuable in your 1st year, so don't be put off by the location of your classes. A lot of people actually enjoy having that separation between 'home' and 'work'- same reason why east-based students might live on west, or vice versa.
As for what block to choose? People don't really segregate themselves by subject like at some other unis. I lived in Fairfax (Vanbrugh) which I think was a good 'half way' point between the uni and Kings Manor for archeology students, but anything west campus is walkable