The Mitre Tavern is touted as the oldest building in Melbourne and has stood on this site since 1868. A classical Gothic facade on the outside, and low doorways, and undulating floor, inside a testement to its age.
Melbourne has some really good Irish bars, and The Irish Times on Little Collins Street is no exception.
The QT Hotel on Russell St, where the Greater Union movie theatres used to be, has a modern rooftop bar called Rooftop at QT.
A couple of kms up Lygon Street, about 25 minutes on the after work peak hour tram, is a small brewery called Temple Brewing.