Goodman was mayoress of Auckland City during the mayoralty of her uncle Sir Dove-Myer Robinson, as well as an Auckland city councillor for 12 years. She was married to former Auckland City Councillor Harold Goodman, who became deputy Mayor of Auckland City in the late 1970s. In 1973, she opened a therapeutic pool at Kingseat Hospital.
Her husband died on 16 August 1988 and she succeeded him onto the council in a by-election, representing the Citizens and Ratepayers group. She championed causes including homosexual law reform, abortion rights, the volunteer movement and campaigned for the Odyssey House Trust for drug rehabilitation. She served as Odyssey House (Auckland)'s Chairperson, overseeing a range of specialist programmes for adolescents, parents, and other adults experiencing serious difficulties with substance abuse, gambling, and other associated problems. She opposed the New Zealand government's plan to build a $500 million rugby stadium on Quay Street in Auckland's waterfront area.
Goodman was the niece of former Auckland City mayor Sir Dove-Myer Robinson, in whose honour she spearheaded a memorial sculpture in Aotea Square, which was built in 2002. The sculpture celebrates the contribution "Robbie" made to the city.
Following Goodman's DBE in 1989, her cousin Lesley Max was made a Dame Commander of the New Zealand Order of Merit for services to children in the 2010 New Year Honours. It is understood to be the first time two Jewish cousins were both made dames.
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- Papakura, N.Z : Kingseat Jubilee Editorial Committee (1981). Kingseat Hospital, 50 years, 1932-1982. Retrieved 5 January 2012.
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- "'No' cause unites traditional foes in the waterfront stadium debate"
- The London Gazette: . 30 December 1988. Retrieved 22 June 2013.
- 20 Year Anniversary of Volunteering Auckland
- Thompson, Wayne (9 April 2001). "Life-size tribute to 'Robbie' planned for Aotea Square". New Zealand Herald. Retrieved 26 May 2013.
- New Year Honours List 2010. Department of the Prime Minister and Cabinet. Retrieved 22 June 2013.
- Benjamin, Henry (19 January 2010). "Nothing like a Dame". J-Wire: Jewish Online News from Australia and New Zealand. Retrieved 21 June 2013.
- Dearnaley, Mathew (22 June 2013). "Late ex-mayoress battled for civic beauty". New Zealand Herald. Retrieved 22 June 2013.