York is renowned for having an excellent variety of pubs and bars (it's one of the reasons I decided to move here in 2000!). The website http://www.yorkpubguide.com/ currently has information and reviews on 256 such establishments, but if you're only visiting for a day or two, you probably won't have time to try them all. So, let me make a few suggestions:
The Last Drop [yorkpubguide.com]
If I'm not at home on a Thursday night, then I'm probably at The Last Drop, chewing the fat with the ioko crowd and enjoying a pint or two of Terrier. This quiet city-centre pub has no fruit machines, jukeboxes, pool tables, children, or other distractions. It does, however, have half a dozen real ales, mostly from the excellent York Brewery range.
Lendal Cellars [yorkpubguide.com]
Would be one of Jocelyn's favourite pubs were it not for the way that the fag smoke hangs around beneath the low ceilings. But what do you expect from a subterranean pub lurking within some cellars between the Mansion House and the Post Office? Still, it has bags of character, decent ales, and does a good range of hearty pub grub, so well worth a visit.
The Maltings [yorkpubguide.com]
The Maltings consistently ranks as one of the most popular pubs in York, despite the fact that its small size limits the maximum occupancy at any one time to 4 adults and a whippet*. Poky it may be, but this place is packed tight with character, humour, and some expertly kept guest beers which you're unlikely to spot in the bigger places. Close to the train station too, so a good place to pop into whilst waiting for your ride home.
*OK, so I'm exaggerating. Slightly.
Tap and Spile [yorkpubguide.com]
Our local, and we kinda like it - fairly quiet of a weekday evening so Jocelyn and I occasionally pop here to chat, read the papers and maybe even sit in the beer garden in more clement weather. Again, a reasonable range of ales on offer (are you beginning to realise what the primary criterion is for inclusion in this list?)
Ha! Ha! Bar [yorkpubguide.com]
Ha, tricked you! Not a real ale in sight at this shiny and slightly expensive city-centre pub, conveniently situated between Coney Street and Davygate. Can be a bit busy at weekends but is generally quieter during the week and the daytime when the comfy armchairs, newspapers and coffee can be quite appealing.
Exhibition Hotel [yorkpubguide.com]
I think the Exhibition is underrated and often goes unnoticed, but it's a decent enough pub very close to Bootham bar. They have a surprisingly sizeable and peaceful beer garden to the rear of the building.
Old White Swan [yorkpubguide.com]
A great historic pub with a lovely interior, good selection of beer, and usually some live music or quiz to keep you entertained.