Something of a hidden gem, this gorgeous harbourside park with a sandy beach was once part of the then 206-hectare Vaucluse House estate. Secluded beneath the trees is Greycliffe House, a gracious 1851 Gothic sandstone pile (not open to visitors), which serves as the headquarters of Sydney Harbour National Park. Despite its ominous name, there's really nothing to worry about at Shark Beach – it has a net to put paranoid swimmers at ease.

Visit on a weekday when it’s not too busy: just mums with kids, retirees and slackers taking sickies from work. It's pretty bushy across the harbour at Middle Head too, so it's easy to forget you're in a city here. You can walk here from Bayview Hill Road in Rose Bay along the pleasant Heritage Foreshore Walk, with great views of the bridge and Opera House.