Mr Goodway (Lab), who is also the council's lord mayor, is seeking to re-dress damage to Cardiff's reputation following criticism over its failing social services department and other controversies.
But he was recently at the centre of a row involving a senior officer who tried to boost the leader's image through the pages of a newspaper (LGC, 6 March).
Mr Goodway said: 'We are ambitious for this city and we are ambitious for the council. What this council has achieved over recent years reflects well on the city. There remains a large measure of agreement in this chamber and outside about what needs to be done.