Lots of touristy and proper hiking in the Blue Mountains. I like the cliffs and waterfalls loops at Wentworth Falls.
Random blog with photos https://www.walkmyworld.com/posts/wentworth-pass
Rent bikes and cruise the Olympic site. Or cut through briefly to the Cooks River and ride to the beach.
Walk through the glow worm tunnel in the mountains or find someone to take you canyoning. Eeevblog has a video. (Not public transport friendly)
Walk through the the coal terminal at Balls Head.
Walk the start of the Great North walk. Or the length of the Royal national Park (Bundeena to Otford).
Bike/walk the Seven Bridges loop.
Go snorkelling / swim the various rock pools.
Swim at the North Sydney Olympic Pool (if they finish it).
Visit Cockatoo Island / picnic on some of the small islands in the harbour.
Go up the pylon on the bridge.