Hi,
congratulations for choosing Sydney, it really is a activity packed place,
if your an adrenaline fanatic then visit one of the many theme parks,
catch a ferry to the zoo,
or a ferry to the queensland-esque town, Manly
the sea at Manly is so turquoise and clear its amazing!
for a more serene holiday you should spend a day bush walking out in the blue mountains,
you can explore the many interesting caves, on a guided tour or on your own,
go for a hike to see the "three sisters" an amazing rock formation,
and watch the blue haze of eucalyptus trees float mistily above the tree tops,
for the shopping addict, visit Paddington, Sydney's shopping hub,
where you can find a mixture of chain fashion stores, or unique boutiques.
for delicious food you cant beat, eating out at one of Sydneys many superb thai restaurants is the way to go.
i hope you have a wonderful holiday!