Could not possibly give you a reason for supporting Randwick. My mother always supported Gordon because she was friends with the girlfriend of a player, so she knew half the team back in the 70s, but I was never pointed towards or away from any team in particular. Don't even remember when I first chose to support them; think it was just a case of watching Shute Shield on TV. I do remember thinking Gareth Smith (former Randwick winger and legendary goalkicker) was the best thing since sliced bread at one point though.
The Brumbies, well, I had an affinity for Canberra as a whole after my Dad took me there on holidays a couple of times, and then I moved to Brumbies territory in 2007. Will always cheer for the Tahs though if they're not playing the Brumbies.
Support the Dragons in the NRL, my parents both support them, so did my grandparents; you don't survive in my family too well if you don't. My little sister even went against her mother's (my stepmother) support of the Bulldogs when she realised she'd have more fun watching the games with us if she supported the Dragons.