Headingley can be a good place to start during the day. plenty of pubs in walking distance. you could do the Otley run. starts in headingley and works its way into the city centre with plenty of pubs on the route. Headingley is about 5 mins in a taxi from centre.
If you just want to stay in the city then there's plenty of pubs and bars. Call Lane is a great area for bars, with it being a stag do entry in to some may be difficult though, all depends on numbers etc.
Oceana could be a good last stop if clubbing isnt high on the agenda.