Northern Quarter is probably your best bet if you want to do a bit of a crawl without walking big distances, but it can get pretty packed in a lot of places at night.
Not sure if all of these places are still going but Briton's Protection, Peveril of the Peak, Lass o Gowrie..aren't too far from where you are staying. They're quite well known real ale pubs with a lot of info on the internet about them.