The Rocks, an Opera House tour, the Royal Botanic Garden to Mrs Macquarie’s Chair, then a sunset ferry.
Day 2
Art + inner city
Art Gallery of NSW and Sydney Modern, lunch in Surry Hills, then an evening in Potts Point.
Day 3
Beaches
Walk Bondi to Coogee in the morning, swim at an ocean pool and keep the afternoon slow.
Day 4
Manly + north
Ferry to Manly, walk to Shelly Beach, or continue to the Northern Beaches and Palm Beach.
Day 5+
Go further
Blue Mountains by train, Royal National Park, or a Hunter Valley day; add Lakemba for dinner.
Honest thought: December heat and UV make middays tiring. Walk early, keep museums for the afternoon and leave room for a swim. Two days give the harbour; five add beaches and the bush.