Pippa and hubby take to air above Sydney

Pippa Middleton is doing Sydney in style on her honeymoon with a run in the shadows of the Harbour Bridge, a seaplane flight to an exclusive restaurant for lunch, and five-star views of the Vivid light festival.

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Middleton and new husband James Matthews landed at Sydney airport on Tuesday night after initially holidaying on the private French Polynesian island of Tetiaro following their May 20 wedding.

They reportedly flew into Australia from New Zealand.

The celebrity couple is rumoured to be staying at the Park Hyatt in the Rocks, which offers panoramic views of the harbour.

The keen runners started Wednesday with a morning jog before later boarding a water taxi which took them past the Opera House to Rose Bay.

There they jumped on a Sydney Seaplanes flight to the secluded Cottage Point Inn for lunch.

The restaurant, frequented by the rich and famous, is nestled in Ku-Ring-Gai Chase National Park.

The inn’s new owner, Ally Olesen, had no idea they were coming until the press descended on the waterfront restaurant which has previously entertained the likes of Westfield chairman Frank Lowy, Dustin Hoffmann, Jerry Seinfeld and Cameron Diaz.

“It’s chaos,” she told AAP on Wednesday.

“We’re surprised and flattered they chose us – we’re very lucky.”

The couple’s seaplane returned to the Rose Bay wharf about 4pm as a light drizzle fell.

Middleton offered up a friendly wave to waiting photographers and reporters before the group again climbed aboard a water taxi.

Pippa is the younger sister of Kate, the Duchess of Cambridge.

After their lavish wedding, the couple initially honeymooned at The Brando, a luxury resort on Tetiaro.

Kate’s brother-in-law, Prince Harry, is due in Sydney next week.

Harry will officially launch the countdown to the 2018 Invictus Games on June 7.