I'm here with a free day...took the free circulator bus to see the town and lo and behold, at the terminus at the University, there was the Botanic Garden! It's free and well worth as much time as you care to spend...I had about an hour and really enjoed it all, especially the rainforest sections. There's a rose garden, lily pond, dryland section, forest section, plus shade gardens as well. Quite lovely and a wonderful place to walk in the shade of the trees.
If you come to Wollongong, I suggest adding this to your to-do list!
Also I really enjoyed lunches at Dunes and Diggies on the beach.