While by no means exclusively so, Newtown is popular with the gay community. Once the stronghold of the Greek community in Sydney, Newtown still has some Greek residents, coffee and cake shops, delicatessens and restaurants. It is on a train line, so you can catch a train from the city, walk the main street and stop for a drink or a meal, and get a bus or taxi back. City Road carries very heavy traffic and parking is hard to find, so don't bother driving there during the day. While you are in the area, Sydney University has an imposing stone main building surrounding a grass quadrangle and housing a fine Great Hall.
Visitors are free to walk around.