Ha Parkette, I've just done the exact opposite and swapped Melbourne for snowy Quebec!
For a cheap way to have a nice drink Melbourne, I would recommend buying some beer/wine and enjoying it in a park (Carlton Gardens, Fitzroy Gardens, etc). If it's a nice day I can guarantee it will be just as good as a bar. Footscray is also an awesome place to go for cheap market food, and I second the Queen Vic market suggestion. If you go near closing time everything gets super cheap.
Cycling is a great way to get around, and it's a really easy city to ride in. The bike hire scheme isn't ideeeaaal, mostly due to needing a helmet, and having a 30 minute limit. If you need a bike you can probably just borrow mine for 2 weeks, it's just sitting at home feeling neglected.
Also, if you do get roped in to going out for dinner/drinks here are some cheap(er) suggestions:
- Killiney Kopitam, Lygon St, Carlton. Singaporean restaurant, most meals <$10
- Ajisen Ramen, two locations in the CBD: Bourke St and Central. Japanese ramen noodle place, mostly <$15
- Houndstooth, Johnston St, Fitzroy. Does fixed price courses, ie $20 for two course, $25 for three, $30 for four. Two is plenty, and the food is always great. It also has long dark wood tables and nice lighting so you feel like you're spending a lot more.
There is also heaps of cheap Asian food, pubs tend to have cheaper nights during the week (if you like craft beer Dejavu Bar in the city does $6 pints on Wednesday nights).
I will update you if anything else springs to mind! Enjoy the (relative) warmth!