Born in Auckland on 5 October 1932, Goodman was educated at St Cuthbert's College.[1] She married Harold Goodman in 1954, and the couple went on to have three children.[1]
Goodman was mayoress of Auckland City during the mayoralty of her uncle Sir Dove-Myer Robinson,[2] as well as an Auckland city councillor for 12 years. Her husband, Harold, was an Auckland City Councillor and he served as deputy mayor of Auckland City in the late 1970s. In 1973, she opened a therapeutic pool at Kingseat Hospital.[3]
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 was patron of Volunteering Auckland for many years.[5] In 2006, she opposed the New Zealand government's plan to build a $500 million rugby stadium on Quay Street in Auckland's waterfront area.[6]
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.[8]