This weekend, that's exactly what the royals did, as William explained in a speech Sunday night in Mumbai, where he and his wife attended a red carpet party at the grand Taj Mahal Palace Hotel.
"Two children and five years later, we have finally made it and we are both honored to be here," William, 33, said.
In his remarks, the royal thanked the many attendees and performers for a "stunning evening" and offered his family's condolences for the recent fatal fire at a temple in Kollam. He spoke of the United Kingdom's historic connection with India – and, now, a partnership between the nations.
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"It seems fitting that Catherine and I start our journey from here, a short distance from the place marked by the famous Gateway of India, where so many people, including my great-great-grandfather, have arrived."
Of course, their trip has not been all black-tie affairs. The couple took time on their first day to play a game of cricket, where Kate, 34, batted and fielded in a tunic-inspired dress, by Mumbai's Anita Dongre, and a pair of sky-high wedges.
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Kate's Sunday ensemble also had local influences: She wore earrings by Indian jeweler Amrapali and the gown's beading was done in India.
As William said that night, "Catherine and I embark on a journey to get to know the vibrant India of the 21st century. An India whose traditions, culture and civilization go back thousands of years, and yet co-exist with an India that is young, creative, entrepreneurial an economic, cultural and political powerhouse, and an established democracy under the rule of law."
William also thanked the British Asian Trust, the charity founded by his father, Prince Charles, for helping organize Sunday's event, which raised funds for several children's charities; and he highlighted the work of three Indian charities in "working to overcome severe problems that many young people face."
"On a personal level, Catherine and I are full of admiration for this diverse and democratic society," he said. "No one can come here without being awed and amazed; no one can come without a sense of excitement about all that India has achieved in the past and the extraordinary promise it holds for the future."
Reporting by SIMON PERRY