On the face of it, Sydney has the most comprehensive public transport network of any Australian city, and this includes a substantial network of commuter rail services (Sydney Trains), train connections at Sydney International airport, and a growing light rail network. A futuristic monorail ran in a loop around the city centre, although this was dismantled in 2013 due to low ridership, and the inability to make the service compatible with the light rail.
Needless to say, Sydney’s most famous landmarks of the Opera house and the Sydney Harbour Bridge are easy enough to visit on foot, and the bridge itself might carry an 8 lane highway as well as a 4 track railway, but you can also walk across it or indeed over it (as a tourist attraction), and that has to be the best option!
Within the urban area of Sydney, you will find some famous beaches, most notably Bondi beach, which is easy enough to get to by bus, or by taking the train to Bondi junction and then walking the last half mile.
Should you rent a car in Sydney? Yes, it will probably be handy for at least some of the time.