The prince is a helicopter rescue pilot in the Royal Air Force, and he's now at a base just off the coast of northwest Wales.
Kate Middleton, now the duchess of Cambridge, is there with him. She does the couple's shopping while William trains and works on the base.
"They don't get bothered at all here," said Daisy Gibson, a 19-year-old university student. "There's rumors about where they are, but nobody knows where they live really. They don't get recognized that much when they go out because they look quite low-key when they walk around."
The couple are able to move around freely in Anglesey, but there is normally at least one "protection officer" discreetly nearby.
According to palace officials, the couple decided to postpone their honeymoon weeks ago.
"They're waiting for the hoopla to die down," said a spokesman who spoke on condition of anonymity in line with the palace's policies.
The palace says it will take place later at an undisclosed location.
The Associated Press contributed to this report.