If you're in the city and looking to flex your brain then why not stop over at the chess room in the State Library of Victoria? Tucked away on the second floor is one of Melbourne's hidden gems. There are eight or nine tables set up with chess sets and another board with Chinese chess, or Xiangqi, can be found there.
Players are always there in the afternoon and it's very easy to get a game. Simply sit down at a chess board and wait for somebody to approach you or just ask somebody who's already waiting. The atmosphere varies greatly from day to day. I've played against very strong competitive players and people just learning the game.
The regulars are always happy to help newcomers to the game and inside the chess room is an enormous chess library with over ten thousand books on chess strategy, openings, middle-games, end-games, tactics, psychology, you name it. If you're serious about chess and are looking for somewhere to prepare for tournament play then the resources you'll have in the chess room are some of the best in Australia.
You'll find someone for whatever your skill level at chess is and I've found the chess room to be a nice place to duck away to when I've had a few hours to kill in the city. Make sure to keep this place on your radar for the next time you're in the city.