bthotugigem05 is there now so he'll be more up to date.
All of my Sydney knowledge is 5+ years old but I did live there for 12 years so, here you go:
You must take the Manly Ferry both ways. Preferably one-way in the day and the other direction at night.
These restaurants in the CBD were great:
Spice Temple
Steersons
Mr. Wongs
In Manly, I love Wockbar, 4 Pines and Fratelli Fresh is a nice stop for gelato.
4 Pines Pale Ale is the best beer in the country as far as I'm concerned. James Boag's Premium is next best.
If you like Red wine, don't drink any Cabernet that isn't from the Coonawara Region in South Australia.
I think the only major tourist attraction you left off the list is Taronga Zoo.
I do recommend the Manly to Spit walk and I don't think it's quite 10 km but, it is very technical. Lots of ups and downs.
https://www.sydney.com/things-to-do/nature-and-parks/walks/spit-bridge-to-manly-walkIf you're looking for something more cruisy, you can hike around North Head just stay away from the edge of cliffs.
If you're in Manly, one that I personally enjoy is the walk from Queenscliff down Steyne Beach to Shelly Beach.
And if you go down to Bondi, I recommend starting on the north side of Bondi and walking at least down and around to Tamarama.
If you just want to have a good time and get drunk with locals without getting in a barfight, I'll give away my local - Collaroy Beach Club. Since you live outside the local 5km area, you're eligible for a temporary membership.
https://thebeachclub.com.au/Enjoy!