Its Adelaide not Sydney!
People need to realise the desire to buy real estate so close to the city is not so important in Adelaide. I can understand in Sydney where the suburbs sprawl and the traffic is bad. But Adelaide is a 30 minute city. If you live within 10km of the city you can get there in 30 minutes on Bus (quicker on tram/train) and even quicker in the car. If you do decide to drive to the city, parking is comparably cheap and easily free after hours and on weekends.
Dont take my word for it, look at the value of some of Adelaides outer metro suburbs, along the coast and foothills. People are obviously prepared to pay for this life style.
Those suburbs that are inner city (North, East and South) are not expensive simply due to their proximity to the city, but its the surrounding amenities. e.g unley and Unley Road, Norwood has its Parade, North Adelaide has its strips etc etc. Then you have all the nice parks, leafy streets, nice schools etc in these areas.
The Inner city Western (and North Westerm) suburbs (Bowden, Brompton, Thebarton etc) are semi industrial, look horrible and for a very long time (if ever) wont match the nice feel of Adelaides premier suburbs. These suburbs dont have as much going for them in terms of quality family living, but will certainly appeal to young professionals and renters.
My advice is to pick a feel good suburb within 10km of the city. I live within 8km of the city and my suburb makes the likes of Thebarton look well..... pretty awful.