Every exchange student in Sydney arrives with a budget and abandons it in the first fortnight. Rent takes most of it. What is left does not cover the version of the city that appears in the recruitment brochure, and there is a stretch around week four where it seems like the answer is simply to stay in.
It is not. The answer is the ferry. A single trip to Manly costs less than a coffee near the university, runs every twenty minutes, and passes everything the harbour cruises charge sixty dollars to show you. Do it at seven in the evening and you have the deck largely to yourself.
By the end of the semester I had taken it enough times that the crossing stopped being an event. That turned out to be the point. The city that costs a fortune is the one you visit; the one you can afford is the one you end up living in, and it is mostly outdoors, mostly free, and mostly reachable on a transport card you already have.