I loved Sydney when I was on holiday there, I found so much to do. It is surprisingly clean for such a large city.
The botanical gardens are beautiful, I had a wonderful day strolling through them and enjoyed a picnic in the grounds.
Going against the grain I thought the Opera House was stunning, I went on a tour of it and found its history interesting, returned for an orchestral show one evening and was blown away.
The bridge is not pretty, but the views from the bridge climb are great, especially when doing the climb at the right time where it gets dark at the top so you see Sydney by night on your way down.
Beaches were pretty, although crowded.
Public transport was clean and reliable.
Sydney is a good base to visit the Blue Mountains from by train and to take ferries to Manly.
I visited museums, Sydney tower, the Sealife centre, the attractions around Darling Harbour.
I found many decent restaurants for evening meals and enjoyed the nightlife, The Ivy was a good club. The food I had in China Town was delicious.
The shopping centres are impersonal but interesting as fairly different from the UK, particularly the food courts and all of the sushi offerings available.
I walked a lot and didn't feel unsafe. People were friendly. It can feel extremely busy at rush hour times though, which felt disorienting and wasn't a nice time to travel.
I travelled with my dp at the time, pre-kids, which would make a difference if I were to return with my family now.
I haven't been to Melbourne so can't compare as pps have.