A burglary was also reported at the Oratia Superette on West Coast Rd in Oratia, near Glen Eden, West Auckland.
A witness said at least one window had been smashed in that incident.
The overnight incidents come just days after authorities confirmed that a new city centre Police base will be created in Auckland in a bid to fight the high rates of crime over the past few months.
A site previously used by its managed isolation and quarantine staff will be opened in about six weeks and would act as a base for about 40 police officers who will start and end their patrols closer to the city centre.
Police are urging anyone with information relating to any of those incidents to contact authorities immediately.