They are in America to hand out awards for their Earthshot Prize - given to innovative ideas for the environment.
But the trip risks being overshadowed by a racism row involving Prince William's godmother.
Lady Susan Hussey resigned after asking a black British charity boss where she was "really" from.
Prince William's spokesperson has said "racism has no place in our society".
This is the royal couple's first big international appearance since the death of the Queen, and since they became the Prince and Princess of Wales.
The royals later visited Roca, a charity supporting disadvantaged young people at risk of or involved with urban violence, praising their "incredible" work.
The couple were introduced to Molly Baldwin, chief executive officer of Roca, who founded the organisation in 1988 to work with a small group of high-risk young people.
William said: "It's trying to get the message across that there's a grey area between when you look at a young person and see a gap between the potential they have and the trouble they cause.
"As a society how do we tackle that? There is so much happens in between and there is so much potential there."
William and Catherine took their first walkabout of the trip in Chelsea, which is close to Boston, where they received an enthusiastic welcome, with one young woman collapsing in tears.
Later in the day, they toured the Boston Harbour Defences with the mayor of the city, to hear about how the area is contending with rising sea levels.
Five winners of the Earthshot Prize will be announced in Boston on Friday - each of whom will be given £1m ($1.2m) to develop their environmental projects.
The awards ceremony will be a mix of good causes and entertainment - performers include Billie Eilish, Annie Lennox, Ellie Goulding and Chloe x Halle.
Environmental campaigner Sir David Attenborough will voice the opening of the ceremony.
Prince William has said the Earth is at a "tipping point" and the awards are intended to support innovative ways of reducing environmental damage.
Watch: Gleeful 8-year-old meets William and Kate