Kibble Palace and Main Range, the incredible glasshouses, feature flora from all over the world and include an exhibition detailing the history of the Botanics.
Even if horticulture isn't your thing, the gardens are just a lovely place to have a picnic or a walk, either on your own or with friends. You can also find little hidden gems, like the now disused railway line, or the ingenious crocheted bench.
When I first moved to the city and didn't know anyone, I would just come and sit with a book. Now, it's a perfect place to come for a walk with a friend, or just to kill a few hours with an ice cream and a walk.