Hi Antoine, welcome to DB!
You're living in Mosman? Ah, my old stomping ground

I lived in Neutral Bay close to the Oaks but my girlfriend at the time had an apartment in Myagah St (I think... testing my memory here!) just opposite the Alan Border oval. These days I call Brissy home, it's good - my New South Welshman DNA automatically makes me superior up here rofl
Shelley Beach is absolutely awesome! If you go down to the beach and swim out sticking to the right hand side there's tons of boulders that have a myriad of sea life - fish, sea horses, cuttlefish, small sharks and a couple of resident Blue Groper. Out in the middle somewhere there is a motorbike sitting on the bottom, it's pretty cool too.
If you go up to the carpark southern end there is a goat track that goes down to a rock platform - this is Fairy Bower. On a calm day you can easily jump off the rocks into about 3m depth which extends to about 18m from memory. Lots of interesting terrain there but you have to be careful of tides, swell etc.
One of the other beaches around the inside of Manly, in the harbour (further around from the pier/oceanworld - maybe Fairlight?) has some great things to look at too.
And of course it goes without saying that absolutely MUST dive with a buddy. There's tons of people on the Northern Beaches, get in touch with Sydney Freedivers to track some down.
And if you're super keen for some depth, Watts and I used to dive at the Spit on the Western side of the bridge. If you like to tangle with Bull Sharks in 30cm of viz then that's your place
Hope that helps!
Cheerio,
Ben