Wellington has the annual Big Look See, which I think missed the mark a bit (or at least appealed to a demographic other than mine).
Auckland has had its Walk of Art for some time now - evidenced here, in hotel/motel pamphlet racks and in occasional small ads in the entertainment section of the Herald over the last few years.
Portland Oregon has an annual trawl of its art galleries as part of the quite good Portland Art Focus programme/marketing cartel.
But this Saturday, if you happen to be sifting around New York, head over to the Bond No. 9 New York Boutique, and jump on board the Passport to the Arts tour. Not only do you get a handy excuse/motivation to visit all those galleries you never manage to get to on the few hours they're open on Saturdays (which seems to be becoming more popular in Wellington than the Moore Wilson's cold meats section), but you get your very own passport full of tiny little artist editions in the forms of stamps. How's that for incentive?