A look at Hahndorf is a nice way to spend a day. The houses are tiny. Like Hobbits had built them. Watch out for your wallet, though! Those retailers will suck every last cent out of you if they can.
Depends how long you're there for.
If you've got a spare couple of days you could head down to Mt. Gambier for a bit of a look. Or up to Coober Pedy.
South Oz tourist maps & stuff
Edit - Hindley street for after dark entertainment. I wonder if "The Venue" is still running? Did a few gigs there over the years. Same place, different name maybe?