Originally Posted by
bseller
I took a guided tour on my first day in SYD which, while a bit expensive

, turned out to have been a GREAT way to get acclimated to the geography. Maybe give that a try!
You can also use the Red (Sydney Explorer) and Blue (Bondi Explorer) buses - hop-on/hop-off or just stay on all the way round. A good way to get a relatively-cheap tour of Sydney, with commentary thrown in.
Sydney and Bondi Explorer