Stillman was educated at Glen Waverley High School (1966-1969) and Sydney Boys High School (1970–71), then graduated with First Class honours from the University of Sydney, and earned his Ph.D. from the John Curtin School of Medical Research at the Australian National University.
Also nearby, but not associated with Sydney Boys and Girls High Schools, are Fox Studios Australia, the Sydney Cricket Ground, and the Sydney Football Stadium.
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Sydney Boys High School also owns and controls properties and other interests at Abbotsford (a rowing facility) and Malabar Headland (the ANZAC Rifle Range).
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He attended Sydney Boys High School playing alongside 1991 World Cup Winning Australia rugby union coach Bob Dwyer and premiership winning St. George Dragons rugby-league halfback George Evans (1962, 1963, 1964, 1965).