As an American who lived in Adelaide (just off Melbourne Street) for 6 months I have a bit of the tourist and a bit of the resident in me.
Adelaide is a great city with a lot to offer, but still has a long way to go before it's a tourist hot spot.
With great museums, the Botanical Gardens, the Zoo, Monarto and Cleland wildlife parks, one of the greatest wine regions of the world, and a culture of the arts - Adelaide has a few niche tourism areas to focus on.
You've also got great restaurants and pubs which are terrific to have a nice meal in or to just relax in.
The problems I see with Adelaide drawing travelers aren't really that big.
The airport, though adequate for the amount of travel (at least when I was there in 2002-2003), needs to be expanded and modernized.
There weren't many hotels in the city center or in the surrounding areas. There may be more now, but really it was the Hilton on Victoria Square and the Hyatt on North Terrace.
I'm not sure how the nightlife is now, but I remember it being near impossible to get a cup of coffee after about 11pm in the heart of the city.
I think those are a few of the reasons that Adelaide isn't drawing the travel or as another pointed out, the international sporting events.
Adelaide has some strengths and that's where the focus should be. Food, Wine, Wildlife, Culture.