Tetley's is neither particularly local nor particularly good. IMO, if you want a decent local beer go for a pint of Sam Smith's or a pint of Black Sheep (not quite so local but widely available and very good). There is also a brewery in York itself, the inventively named York Brewery.

Good pubs that are close to the sights and the station that I would recommend include the Ackhorne in St Martins Lane (a small lane just off Micklegate) and the Maltings in Tanners Moat. You'll get a good selection of real ales and a good ambience in both of these.