Sydney in November

In Sydney try to stay near the water. We stayed at the Intercontinental with great views.
Go to the Opera House, out to the Rocks, to a beach. Take a boat around the harbor.
We did not use any tour companies. We went in October, spring, beautiful. Also traveled up north to Port Douglas, Great Barrier Reef area .which is very tropical. , spring, beautiful. We went down to Melbourne too.

What Suki said plus ...

Take a boat around the harbor.

Cheapest option is to catch a public ferry from Circular Quay on what is known as the inner harbour route. It's a ferry route that goes in a circle and takes around 40 minutes and stops at places like Mosman and Neutral Bay.

Also you can catch a public ferry to Manly to go to the beach. It's a longer ferry ride and a great way to see the harbour.

Sydney has a famous beach walk from Bondi to Coogee which follows the cliffs and takes you past a lot of beaches and cafes. It's easy to get public transport to and from the walk.

Sydney also has some really lovely harbour beaches in the eastern suburbs which are great for swimming - Google Redleaf, Parsley Bay and Nielsen Park. Beautiful places to relax and enjoy life.

If you are into hiking then a day trip to the Blue Mountains for a bushwalk is another great thing to do. There are tour companies but you can also easily do it yourself by catching a train to Katoomba, Leura or Wentworth Falls.

For great seafood go to Doyles restaurant on the waterfront at Watsons Bay. Excellent fish and chips. They have been in business since 1885.

I would suggest that you try to stay in The Rocks section. It's the very charming "old town" sector of the city with a number of atmospheric little places to stay. A particular advantage to the location is that it's a short stroll over to Circular Quay where the ferry terminal is located, and which the transportation hub for buses and trains as well - any of which you can access with an Oyster Card which makes getting around about as easy as can be.
Do ride the ferries - doesn't really matter where, though the trip out to Manly is a personal favorite. You can also ride the ferry across the harbor to Taronga Zoo and walk along the pretty shoreline path that is Sudney Harbor National Park, returning to Circular Quay from any of the other little terminals along the way.
Another pretty excursion is to walk thru the Botanical Gardens - located just beyond the Opera House.

transportation hub for buses and trains as well - any of which you can access with an Oyster Card which makes getting around about as easy as can be.

The transport card in Sydney is an Opal card, not Oyster. You can also use an American Express, Visa or Mastercard to pay for public transport so there is no need to buy an Opal card. You need to tap on with your card when you get on the bus or at the train station or ferry wharf and tap off again when you finish your trip.

Ahh ...you're right of course.
Was just in London and so had Oysters on my mind - my mistake.