There are numerous places to watch whales along the east coast of Australia, with roughly May to November being the time to watch their migration here. I opted to take a cruise tour to get up and close to the whales.
There's plenty of whale watching cruises in Sydney. I took one that provides BBQ lunch on the way out of the harbour at $39 per person. I liked the tour guide who was sensitive to the whales and coordinated with the skipper to not disturb the whales in their natural migration.
The whales we saw this time were not very active. The active ones can jump out of the ocean and make a splash. Most of the cruise tours guarantee sighting of whales, but don't guarantee seeing splashing display of whales. Anyways, just seeing the large humpbacks up and close is still quite impressive. Be prepared however to have to wait for a long time to see the whales, especially when they take deep dives (aka down time) that can be many minutes long.
Another unexpected thing I learned from the tour guide is the nudity-allowed Lady Bay Beach that's close to the tip of the South Head. We can see several nude men and women sunbathing on the beach when going past the Head.