William is based as a Royal Air Force search-and-rescue helicopter pilot.
Prince William and Kate with their newborn. (AP Photo)
Wearing black jeans and a grey-green jacket with her long brown hair loose, Kate was described as looking "absolutely gorgeous" by locals who had come to watch the start of the gruelling three-day Ring O' Fire race around Anglesey's rugged coast.
She told one onlooker that she had left baby George with his grandmother, Carole Middleton, for the day.
"I said 'How's he (George) doing?' She said 'He's doing really well, he's with his grandma'," said Sarah Bingham, whose husband founded the race.
"They are both really lovely people, really genuine. It was nice to speak to her after what Kate's just been through. She looks wonderful, doesn't she?"
Members of the public said Kate, 31, appeared to be taking well to motherhood.
"We were talking about the joy she was having from George and how quick he was changing, she couldn't quite believe it. She's enjoying every minute of it," said Marian Wyn-Jones.
"He's getting quite huge, she said."
William, who is second in line to the throne after his father Prince Charles, rang a bell to start the race and clapped with his wife as the runners set off.
The couple are set to leave their Anglesey home this month when William's three-year tour of duty there ends.
He announced this month that his family would be moving "elsewhere", and they are widely expected to return to London.
The prince, 31, did not say whether he would be staying with the air force, but royal-watchers expect him to take on more royal duties as his 87-year-old grandmother Queen Elizabeth II cuts back her schedule.
Prince George Alexander Louis was born in London on July 22.
In an interview last week, William described his son as a "bit of a rascal" and admitted that the new arrival was keeping the couple on their toes.
"He wriggles around quite a lot," he told CNN. "And he doesn't want to go to sleep that much, which is a little bit of a problem."