Sydney:
do the Sydney Harbour bridge walk - even the locals do this as its so cool.
http://www.bridgeclimb.com/
Go to Taronga Zoo - not so much for the animals (which are great) but because they sit on the best real estate in Sydney with fantastic views
for something silly - the Aussie Duck tour. Go to see koalas and then a tour of sydney harour in one of those silly trucks that goes into the water.
http://www.sydneydaytours.com.au/myweb2/kpad1_copy(1).htm
or just go to Circular Quay at the Rocks and grab a ferry for a few dollars and see the harbour yourself-take a picnic lunch to eat at Manly.
Darling harbour for Sydney Acquarium or Maritime Museum.
otherwise a small dive and nothing too challenging?? Magic Point at Marubra if the grey nurse sharks are in, sea horses at Balmoral nets (10ft dive) or weddy sea dragons at Kurnell
http://www.allsydneytours.com/?gclid=CMvu3r64j4UCFU9bIgodHH6tFA for some more ideas
i see that you sing opera - you can do a tour of the place or catch a concert
http://www.sydneyoperahouse.com/
hope this helps and pm me if you have any questions i could help you with
cheers