Fullarton is an inner southern suburb of Adelaide, South Australia in the City of Unley. It adjoins Parkside, Unley, Malvern, Highgate and Myrtle Bank and is bisected by Fullarton Road. Fullarton is bounded by Cremorne Street, Randolph Avenue and Fullarton Road in the north, Glen Osmond Road in the east, Fisher Street, Fullarton Road and Cheltenham Streā¦Fullarton is an inner southern suburb of Adelaide, South Australia in the City of Unley. It adjoins Parkside, Unley, Malvern, Highgate and Myrtle Bank and is bisected by Fullarton Road. Fullarton is bounded by Cremorne Street, Randolph Avenue and Fullarton Road in the north, Glen Osmond Road in the east, Fisher Street, Fullarton Road and Cheltenham Street in the south and Balmoral Street, Fisher Street and Windsor Street in the west.