There are busses and trams which are both FREE! within the city centre
(Note: not all busses are free; if you use the tram outside of the city centre, it’s not free).
Within the city, the tram travels along North Tce (right in front of UniSA’s City West Campus) and down King William St. See here for more detail.
The free bus runs on a clockwise loop (99C) and an anticlockwise loop (99A), around the eastern and southern halves of the city centre. See here for more detail.