The demonstrations, which have featured brief blockades of intersections and bridges, could disrupt traffic during the visit and may raise new security concerns even though there has been no major violence so far in New York.
During the visit, the couple will part ways briefly when William heads to the White House on Monday to meet with President Barack Obama.
The prince also is set to join a Washington conference on illegal trafficking of ivory and other animal contraband.
New York City's first lady Chirlane McCray will escort Kate to meet youngsters at Northside Center for Child Development in Harlem, which provides mental health and educational services to families living in high-risk neighborhoods.
The center, which aims in part to fight racism, was founded by researchers whose pioneering studies were cited in the U.S. Supreme Court ruling Brown v. Board of Education declaring segregation in public schools unconstitutional.
On Monday evening, the royals are set to venture into Brooklyn for a National Basketball Association game between the Brooklyn Nets and the Cleveland Cavaliers at the Barclays Center.
At least one protest is already planned to coincide with the game. A Facebook event page titled "Barclays Stadium, SHUT IT DOWN," has 83 people saying they would attend the rally in the borough.
"Foreign dignitaries are going to be at Barclay's Center tomorrow, so lets shut it (and the mall and Atlantic and Flatbush) down," the page reads, referring to the two main avenues in Brooklyn.
On Tuesday, the royals, who are expecting a second child in April, will tour the National September 11 Memorial and Museum, including its reflection pools.
Dignitaries including former Secretary of State Hillary Rodham Clinton and daughter Chelsea, a new mother herself, are expected to meet the couple.
They will cap their visit by attending a fundraising dinner at the Metropolitan Museum of Art on Tuesday night to benefit the University of St. Andrews in Scotland, where the couple met and earned their college degrees.