My favourite Sheffield boozers - all sell proper beer and the vast majority don't play music (if they do it tends to be live or quiet). If I had the time I'd do a long-winded descriptive list like Roadie but I don't so just the names, locations will and a brief summarisation willhave to do:
The Fat Cat, Kelham Island (legendary)
The Kelham Island Tavern, Kelham Island (ditto)
The Riverside, Kelham Island (wicked Sunday evening acoustic/unplugged sessions)
The Wellington, Shalesmoor (formerly the Cask and Cutler) - astonishingly friendly landlord, no fizzy stuff on tap whatsoever

The Moon, Upperthorpe (my local)
The Red House, Netherthorpe (lovely management, wicked live music boozer)
Fagans, Brook Hill (folk-tastic)
The Dog & Partridge - *very* Irish - 1 side room totally devoted to JFK

The Devonshire Cat, City Centre - modern, diverse boozer with lovely food and the best selection of beer in Sheffield
The Brown Bear, City Centre - Sam Smith's boozer currently closed for 'refurbishment' - campest barman in the world, cheapest booze in Sheffield and the most 'interesting' clientele
I think that's it . . .