Prime Minister John Key says if a visitor levy is proved viable it should be rolled out nationally, not just in Auckland.
Mr Goff's proposed budget for next year aims to keep the average rates increase at last year's level of 2.5 percent. To do so, he wants to raise about $30 million from the accommodation industry.
Visitors to Auckland could pay an average of $5 extra per night under the levy proposed by Mr Goff, who said it could raise the $30m and keep rates down.
It would replace ratepayer funding spent on attracting visitors and supporting major events.
Mr Goff said ratepayers had shouldered the responsibility for the growth of the city and it could not be expected to continue.
Accommodation providers' rates would increase, but they could recover the cost through the levy, he said.
"The accomodation provider, while they get the benefit, won't be paying the levy.
"The levy will fall on the visitor - so a visitor staying at a four or five-star hotel in Auckland, they're probably paying $280, $380 a night, they'll have to pay another $6 to $10.
It is the biggest change likely in Mr Goff's first budget as mayor. His hope the government would approve a regional fuel tax was unlikely to be realised and in place by next July.
The plan will go out for consultation early next year, along with a the mayor's bid to introduce a living wage, which could boost the pay of more than 3000 council staff.
Phased in over three years, the higher wages could cost $9m a year - equivalent to nearly 0.6 percent on average property rates.
Mr Key said Auckland was not the only area facing such problems. A levy should be looked at for all of New Zealand.
He said a working group was looking at the cost of tourism infrastructure and he expected a report from the group shortly.
"If we're going do something in terms of that sort of mechanism, then I think we want to do it nationally and don't think we want to do it locally.
"Auckland may well have some tourism issues, given so many people flow into Auckland, but the reality [is] so does Queenstown, so does Taupō, so does the rest of the North Island."