What an intriguing topic for a thread, love it! If anything because it is, to me, so interesting that so many royals are partial to the US, a nation that's not necessarily partial to the concept of monarchy!
For starters, like most Dutch folk I know that Princess Christina, Queen Beatrix's youngest sister, spent much of her marriage to Jorge Guillermo living in an apartment on New York's Fifth Avenue. Gossip magazines implied that she chose to live far away from her home country to curb exposure of her husband's sometimes aloof behavior, but I haven 't the faintest whether there's even a grain of truth to this. The Guillermo family moved to the Netherlands some time in the eighties anyways, and built De Horsten (where Alexander and Maxima currently live) after which Christina called the whole deal a day around 1990 or so.
Speaking of Maxima, she famously lived in New York city also, in the mid to late nineties, and left the city in 2000, when it became clear that Alexander considered her a 'keeper'. I believe she had an apartment in Chelsea, a neighborhood on the island of Manhattan.
Maxima's current sister in law, Laurentien, lived in the US also, as did Johan Friso and Constantijn at some point. They lived in Northern California's Berkeley, the famous university town near San Francisco. Friso and Laurentien both persued studies there, at the University of California at Berkeley, which is one of the most renowned universities on the planet. This famous liberal-minded, state-owned (as in, by the state of California) university has been the alma mater to a raft of other royals, for example to Norway's future king Haakon. It is said that Constantijn and Laurentien love the San Francisco Bay area so much that they spent much of their honeymoon there.
To go back to New York for a moment, that city of course was once home to one of the princes of Liechtenstein, and also to Marie Chantal of Greece and hubby Pavlos, who, like cousin Felipe, once studied at Georgetown University in Washington, D.C.
And the former Shah of Iran's eldest son, Reza, currently calls the D.C. area home. He lives with his family 'across the river' from Washington, in Virginia, a spot where a lot of middle eastern royalty have homes, too. Case in point: Queen Noor of Jordan.
Speaking of studying in the US, Albert and Caroline of Monaco have spent time studying in America, but I'm not sure where. Anyone know?
And Stephanie lived in Los Angeles, California, for a while in the eighties.
And of course, Victoria of Sweden spent a few years in Connecticut, at Yale University.
Currently living in New York is one daughter of Princess Irene of Oranje, Maria Carolina, who is working for the United NAtions I believe. Any other current royal New Yorkers not mentioned? Or current blue-blooded Californians?