I don't know if its offbeat but if you buy a ferry pass. Its great fun taking the ferries across the harbour to the different places & up river past the old Olympic Stadium which is not quite on the river. You can get off at one stop & dine at a fabulous, I think fish restaurant near the mouth of the harbour & look up through 'The Gap' at the city & loads of other places subject to the timetable. It's worth exploring. You could take a seaplane flight but it is expensive partly due to high maintenance costs. about 8 years ago
There's stack loads! Really depends what your into... These sites are handy (listed in the order of which ones I think are most useful) Checkout:
PS. That Timeout magazine is everywhere in Sydney... Handy to pick up. Especially if your into live music etc.
PSS. I'd suggest buying a weekly travel pass. & If your going on a budget, most of the meals at Fiveo's are $5 and there are plenty of other backpackers http://www.letseat.at/fiveos
Hope that helps a bit :-) Have fun! about 8 years ago