For me, South Australia is all about food and wine. COnducitng your own walking tour around the city is a lovely way to see some of the great churches and tree-lined streets. Stop in early at Central Market to pick up fabulous fresh produce and a bottle of wine for a picnic in the botanical gardens.
For eating in Adelaide some notable places - Auge, The Manse, Farina.
My favourite place for a pre-dinner drink or glass of wine and antipasto lunch is The Apothecary.
If you have time a couple of days on the road up to the Barossa or down to the McClaren Vale are a must. In fact, I'd spend 2-3 days in Adelaide city itself and then spend the rest of the time in the wine country. The Adelaide Hills are also great but we found it harder to drive around here and seemed to always end up down the wrong road and miles away from where we wanted to be (not so bad if you have time and like to explore!).
In the McClaren Vale - don't miss Samuel's Gorge. A lovely little atmospheric cellar door where you can taste the great Shiraz and grungy Tempranillo.
Penny's Hill is also a nice spot to try a good drop or two, but for me it's all about the fabulous lunch in the gorgeous homestead-feel building. Make a reservation! about 10 years ago
Since I have a weakness for asian food, BBQ King in Chinatown is excellent and cheap. There's also $1.50 lassis in the food court. Opposite BBQ King is a supermarket with durians and a bubble tea stall with the best bubble tea I have had in Australia.
I can't remember the exact location, but Adelaide is home to the original Hogs Breath Cafe in Australia. On the same street is an absolutely fantastic chinese dessert place. Again, I can't remember the name, but it's in the near vicinity. Ask a few randoms and you'll probably find it.
Glenelg Beach, whilst it has average surf and is frequented by sharks, is still well worth a visit, and there's a really good icecream shop on the main road... and lovely fresh, raw oysters. Sublime. about 10 years ago