Out of all the free things to do in Melbourne, visiting the Royal Botanic Gardens Victoria is my ultimate favorite.
The park is easy to navigate on your own, with signage that are easy to follow, but to get more context or even learn more, a free guided tour called the Aboriginal Heritage Walk is also an option to consider. A good walking shoes is a must, especially if you are keen to really explore the parks many trails. If you are a family traveling with kids, The Ian Potter Foundation Children’s Garden is just the right place to introduce kids to the beauty of the park.
I went to Royal Botanic Gardens on my own, walked starting from the Flinders Street Station direction and ended my tour at The Shrine of Remembrance. I spent a considerable amount of time inside the park, specifically at the Ornamental lake, watching people navigating the waters on a punt boat ride.
I did not spot any penguins but I consider my visit at St. Kilda Pier a worthy effort. It is a good place to just sit quietly, enjoy the sea breeze and wait for the sunset. The pier sort of reminded me of the movie poster of Never Let Me Go.