The Royal Botanic Garden, Sydney is my favourite botanic garden in the world. While many gardens are condensed, there are vast expanses of space that encourage people to picnic, exercise, eat and drink and celebrate as well as the obvious: to enjoy the plant life.
If you enter the Gardens out by Mrs Macquarie's Chair, you will surely pass Handa Opera and Westpac OpenAir, which is a beautiful entry point and also a great jogging route. Further down are 2 lawns that form a bit of a crescent around one on Sydney Harbour's coves. This is the perfect place to tan, picnic, read a book, etc. As you walk further down, the paths become numerous with a few different choices of what to see. There's a pond with bamboo and Asian gardens. One of the major things I'd like to make note of is The Calyx, which has one of the largest living walls in the southern hemisphere. They use it for exhibitions, events, a cafe and eatery, high tea, etc. It never fails to disappoint. You'll find tropical gardens, entire areas devoted to succulents. Further back into the gardens, you will stumble upon the herb garden and a pavilion; this is so well maintained. Beyond that, you'll see the amphitheatre and another pavilion. Oh, and did I mention the gardens have BATS! Yes, bats! They are a very interesting feature to the gardens. I know I never expected to see bats here. I'd say where they are, but please find them yourself - without the help of the internet. You have a wonderful botanical garden. Enjoy it!
And, if you want to make a full day of it, the Art Gallery of New South Wales, is right across the road from the looped road you will have entered. I think it's the best museum in Sydney, and it amazes me the permanent collection the AGNSW has along with its continuous exhibitions.
Enjoy Sydney!