If you're an arty farty type like me, you'll love the Art Gallery of New South Wales, which is near the Botanical Gardens/Circular Quay/Opera House. You should try and check all of these out! A ferry ride across Sydney Harbous is the best way to view the Operan House and the beautiful views... plus its fun! You can catch a ferry across the harbour to Luna Park (if ur into Theme parks) or catch a ferry to Watsons Bay and have lunch at Doyles Seafood Restaurant on the beach - its stunning and delicious, plus historically interesting - It was Australia's very first fish n chips shop, way back in the 1800's! (I used to work there as a waitress - not in the 1800's, lol, just a fwe years ago :P)
I grew up in the Eastern Suburbs of Sydney (where the famous Bondi beach is located). Dont just visit Bondi, as it can get uncomfortably crowded. Bronte, Clovelly and Coogee beaches are just as beautiful, and less touristy. There is a coastal walk you can do from Bondi to Coogee and back which offers AMAZING views over the Pacific Ocean... its about a one hour walk, so its a good workout too! I highly recommend it :) Just ask one of the locals to point u in the right direction, everyone knows about it.
Hyde Park is really beautiful, as is St Mary's Cathedral (near Hyde Park and the Art Gallery of NSW).
Glad to hear you have already booked in at Bobbi's Pole Studio! Thats where I trained - they are amazing teachers who really know their stuff and are soooo friendly. You'll have a blast! My favorite teachers were Chilli (very vivacious and confident) and Isabella (quiter but very sweet). Cleo is also fantastic, and she came runner up to Felix Cane in Miss Pole Dance Austalia 2011. So she is extremely talented too. :)
If you're in the mood for some retail therapy, Bondi Junction's Westfield is HUGE and offers everything... For Pole STuff, go to highheels.com on Elizabeth st, Surry Hills (you can walk up the hill from Central Train Station).
Hope this helps.... have a great time! :)