"I've heard that the (Auckland) scenery is very beautiful," Ivanovic told the Herald on Sunday. "It's very green with beautiful cliffs and beaches. I've heard about the black (sand) beaches, which I would love to see."
Ivanovic's parents have joined her on this trip and her businessman father Miroslav, who is a golf fanatic, may be whisked by helicopter to Pauanui for 18 holes at the Lakes course.
He is also likely to be offered a round at Titirangi.
Fellow superstar Venus Williams is not known to have made any special requests, but she wowed crowds yesterday at an exhibition hit-out in front of the Auckland Museum.
About 500 people watched the seven-time grand slam winner exchange rallies with Kiwi Marina Erakovic, before she signed autographs and photos for fans.
After arriving on Friday, she planned yesterday to "get out, see the sights and the city experience and kind of be a Kiwi for a day.
"I have wanted to come here for a while and finally I got my chance," she said. "Once I landed I was like, 'I'm here' so I am so fired up to be here. The support at the event (yesterday), people are so into the tennis and they know all of the players ... It's exciting to see the enthusiasm."
Ivanovic and Williams, both playing in their first $250,000 ASB Classic tournament, also attended the official players' party at The Cloud last night.
Ivanovic spent about two hours at the party before leaving at 9pm.
Williams arrived at 9.15pm and charmed party-goers for about 10 minutes before leaving for dinner at Korean restaurant Faro.
