In her first and only speech of the tour, Kate said she was thrilled by how she and Prince George had been received by the public.
"I would like to take this opportunity to thank everyone who has welcomed me and George so incredibly warmly on our first visit," Kate said.
"To be here together as a family has been very special and we will always remember it with fond and happy memories. Thank you for inviting us here and for such a generous welcome."
Kate made the speech during her visit to Bear Cottage, a children's hospice in Manly. William and Kate met patients of the facility as well as the bereaved families of former patients.
"It really is wonderful to be here today - having the chance to meet you all and to see the incredible work of Bear Cottage," Kate said. "First class delivery of children's palliative care is life changing.
"When families are confronted with the shattering news that their children have a life limiting condition, their world can fall apart. It is at those times that professional support is imperative.
"The haven that you have created here is inspirational, and there is so much that you can share with each other as you continue to support and nurture those in your care."
The royal couple's visit to Bear cottage began about 3pm after they arrived to cheers and hoots from the big crowd along Fairy Bower road.
After meeting Mr Abbott and his wife Margie out the front of the centre, the royal couple were escorted inside to the playroom where they split up, with the duchess mingling with kids, while the duke spoke privately with families.
"Very nice to meet you, Daniel," Kate said on meeting Daniel Howarth, 16, who suffers from lung disease and had a Union Jack flag strapped to his wheelchair.
From the playroom, she made a brief visit to the centre's quiet room then ventured outside to the garden to take part in a music therapy class with sick children and their families.
The Duchess sat on a wooden garden bench and played a drum with the children, and also took part in a rendition of Twinkle Twinkle Little Star, before the duke joined her to meet with families.
From the garden, the royal couple took part in an informal afternoon tea where they were presented with an artwork painted by Bear Cottage kids.
Sophie Martyr, 16, was still shaking after making the presentation to the royal pair.
"It was amazing, it was unforgettable," she said. "They're really personable, they're really genuine."
On his way out, Mr Abbott said it was a "fabulous afternoon for Bear Cottage".
"These are magnificent people here. There are some very special and brave kids here," Mr Abbott said.
"To get this visit from Prince William and the Duchess is just extraordinary."
Before getting in the royal motorcade, Kate thrilled the crowd by meeting a number of fans and receiving flowers and a toy footy.