There's no better footy field in Australia and there's no better team than the Wests Tigers. If you get a spot on the famous hill where you can relax on the grass with the local die-hard tigers supporters it'll make the experience even better. Good atmosphere at Leichardt oval and the ground's small so you can experience all the action up close. Even junior games there on the weekend are a great family day out.
Check the NRL site to see when the games are on and you should be able to buy a ticket at the gate (or book online).
If there aren't any games on, you can take a ball and just have a kick around on the field yourself.