I also live in Sydney, and the first question to ask is always "do you have a car?" (and then "how long you here for?")? A car makes it much easier to visit various spots (e.g. the national parks, Mount Annan (https://maps.app.goo.gl/WJRcJY8RHtRLV7Tm9) IMHO is a better botanic garden than Royal (the one in the city) because it focuses on native plants, Blue Mountains/Hawkesbury, the various zoos which are further out), whereas if you don't have a car the city has enough things close by to do. Powerhouse is great (the real one, not the one which is going to flood), Australia museum is great, if you can go on a ghost tour for the Rocks and the QStation. There's lots of other minor museums throughout the city, esp. the Rocks.

I'll be visiting next month so can't comment yet if it is any good, but kayaking Sydney Harbour sounds like a lot of fun.

Lots of tour operators doing it, deals on BookMe and Groupon.