The Mayor of Broken Hill says Australia's first legal same-sex marriage should take place in the Silver City.

The issue has come to the fore after two Australian men were some of the first to be legally wed in New Zealand yesterday.

Mayor Cuy says Broken Hill's unique location and cultural history could see it become a prime destination for same sex couples who want to marry.

He agrees with Barry O'Farrell and Kevin Rudd that the issue of gay marriage should be put to a conscience vote.

"I think whatever a person wants they should be able to do," he said. "I think if they live in civil harmony, they're entitled to that. I don't really see that it's going to hurt anybody. To say that we're actually going to be joined together, I don't see that as a problem. I believe that everybody has a right to live in harmony, and if they want to get married they should get married."

And while acknowledging there'd be considerable local resistance, Mayor Cuy says says there'd be fringe benefits in tourist dollars if the Silver City were to go pink.

"It'd be great for the city if we were to become the first. Given our Priscilla background - and knowing that we have a a very active gay community here - you'd go: 'Why not?'