Your request was answered to the extent that the Department said that it is a property in Bolton St, Wellington, but it wasn't clear whether it was Crown-owned. But another source online confirms they are (Footnote 1)

Because you probably hadn't preconceived that they would respond to you with a street name and no address, you hadn't therefore specified an address. As such the didn't need to disclose the number to answer your request, as your request had been answered by asking 'what is the official residence...'.

If you did want to know the street number of name of the residence (considering those other official residences do have names), then you could do so.

They have made a position that they wanted to withhold the that information based on those two grounds of privacy and improper pressure/harassment.

I think their position is incorrect.

To start with, although they don't specify the addresses the other official residences they name, the street addresses can be found (see footnote 2). While they did not disclose who lives at these other residences, it can be found from online sources (FN 3) . For example we know the Prime Minister's official residence is Premier House.

So you have to question, why they want to withhold the street address for the Bolton St property, given the street addresses for other properties can be found.

Online sources reveal that the Bolton street address is likely to be 23 Bolton St. (FN 4). This property is owned by Her Majesty The Queen, who is the living embodiment of the Crown (FN 5).

Turning now to the actual withholding provisions. I could drill right down into the Ombudsman's guidelines for 9(2)(g)(ii), (FN 6), but will just make some salient observations instead.

"“Improper pressure or harassment” is something more than ill considered or irritating criticism or unwanted publicity. It is a course of conduct that has such an effect on the person against whom it is directed that he or she is unable to perform his or her duties effectively and hence the conduct of public affairs is at risk."

"If the section is to apply, there must not only be a
reasonable likelihood of improper pressure or harassment".

and...

"The agency must demonstrate that the prejudice or harm is so likely to occur that it is necessary to withhold the information in order to prevent that prejudice or harm from occurring. A mere possibility that prejudice could occur is not sufficient to meet the requirement under section 9 that withholding is necessary."

So was there a likelihood of the harm occurring -- has this Minister or other Ministers been unable to carry out public affairs when the address of an official residence been released? Is there precedent? DPMC didn't refer to any such matters.

In respect of the withholding for privacy, the strength of privacy interest is low. Other residences, such as Premier House especially, are known to house particular Ministers. The fact that that they confirmed he lives at a Bolton St property, that 23 Bolton St is in the public domain, and that it is an official residence, not a private one, reduces the privacy interest.

As an aside, from looking at the information online there is actually a whole lot more information held by DIA about the Crown's property portfolio for ministers. (FN 8)

Footnotes

FN 1: https://www.beehive.govt.nz/sites/defaul...

FN2: https://en.wikipedia.org/wiki/Vogel_House

http://www.newstalkzb.co.nz/news/politic...

FN 3: https://en.wikipedia.org/wiki/Premier_Ho...

FN 4: see below

page 3: https://www.parliament.nz/resource/en-NZ...

page 160: https://www.parliament.nz/resource/mi-nz...

https://www.gets.govt.nz/DIA/ExternalTen...

FN 5: https://gis.wcc.govt.nz/LocalMaps/Viewer...

FN 6: http://www.ombudsman.parliament.nz/syste...

FN 7: http://www.ombudsman.parliament.nz/syste...

FN 8: Page 160 at https://www.parliament.nz/resource/mi-nz...