I know these places are promoting the event but I am sure there are others.
Heineken Beer Garden
Outside the Grand Slam Oval
Melbourne Park, Batman Avenue
Crown Sports Bar
View schedule here
131 Queen Street, Melbourne
Not advertising but worth a try is
Charles Dickens Tavern
290 Collins St, Melbourne
The Builders Arms Hotel ( 211 Gertrude St, Fitzroy) and the Albert Park Hotel (Cnr Montague St and Dundas Place Albert Park) screen the Aus Open every day for the duration of the tournament.
The Emerson (145 Commercial Road, South Yarra) holds Aus Open events with tennis themed cocktails and has two 80 inch screens to take in all the live tennis action from Melbourne Park.