Can't speak to Italian immigrants, but Jewish immigrants mostly stayed because of the thriving Jewish infrastructure they had available and because they were primarily urbanized in Europe. For all that the "shtetl" is the archetype of European Jewry in the prewar period, while it was certainly a phenomenon, Jews urbanized very quickly when given the opportunity and so it is natural that they chose to remain in a city.

The value, in general, of immigrant networks in the history of immigration can't be underestimated. For Jews, those immigrant networks were called "landsmanshaften," and they consisted of a brotherhood (most early immigrants were men, many of whom brought families with/after them) society in which these Jews prayed, socialized, found out news about their hometowns, took advantage of connections/opportunities from people who had come earlier and "made it," and sent money back to the home kehilla (community). Landsmanshaften provided services from birth to death (if you go to most NY area Jewish cemeteries you'll see sections owned by landsmanshaften in which generations of local Jews were buried) and were an incredibly valuable resource for a young immigrant eager to take advantage of the "goldeneh medina" (golden country).

Those immigrant networks weren't the only support systems in place incentivizing Jews to stay in New York- there were large charitable networks providing financial assistance, medical care, assistance with immigration authorities, childcare, and more. Many of these networks were actually run by Jews- first by acculturated German Jews who had come in earlier waves of immigration, then by newly acculturated Eastern European Jews. All of this combined with the large number of synagogues, easy availability of kosher food, vibrancy of Yiddish culture, and proximity to other Jews and place in a large Jewish collective were reasons why New York was an attractive option.

The fact that New York was urban was of course important as well- and not just urban but a center of manufacturing and sales. As mentioned above, Jews urbanized very quickly, with major cities in Eastern Europe acquiring large minorities of Jews often very disproportionate to their part of the population. Even small-town Jews were more likely to work as craftsmen or tradesmen than in agriculture, which was more the sphere of the Christian majority in Eastern Europe. Therefore, when coming to New York, Jews were well equipped to join the workforce, particularly working in factories (often in the garment industry).

Now, technically none of this means that Jews couldn't have ended up in other urban areas- or even small towns- and the fact is that many did. But New York, for the reasons listed above, remained popular, with immigrants arriving at Ellis Island and, seeing no reason to leave, staying put. And, of course, as these new immigrants stayed, Jewish communal ties and organizations only became stronger and stronger. Other cities developed similar infrastructure over time, including landsmanshaften, and there were efforts by some charitable organizations to prevent overcrowding by having Jews immigrate through Galveston and settle cities in the South and West. Yet New York remained, and to this day still remains, by far the most popular option for Jews in the United States.