City Pubs with accommodation are not as common in Ireland as they are in the UK. They are a little more common in rural areas.
The only one I can think of in Cork city (and in fact it's not right in city centre but about 10 mins walk to centre) is http://handlebarsguesthousecork.com/about.htm (Handlebars Guest House)
It is across the road from the cork railway station (Kent Station)
I can't comment on how good it is as I don't know anyone that has stayed there.
There are no B&B's right in the city centre. The majority of them are about 5-10 mins walk from the centre and there are plently of them, and very good ones too.
There are a few hotels that are right in the city centre and they would have a bar attached. These are:
The Victoria (wouldn't recommend it)
Any others are 10 mins or more walk from centre.
Edited: 10:43 am, January 06, 2013