So Donna Gabaccia has done a fair amount of work in this area and the answer is complicated.

Most Italian immigration in the years preceding he Risorgimento was to one of two destinations: Argentina or the United States. Most of this was from the North (for example the head of the Italian department at Columbia University was Felice Foresti who had been a prisoner of the Austrians after the revolts of 1848 in the Veneto), the only cases of exiles from the south I know of went to Britain or France (Mazzini famously fled to Paris). Some, like Garibaldi, famously toured both in exile.

Most immigration between the Americas and Italy stopped in the 1860’s as there was a fair amount of conflict going on in both Italy, with unification and the wars associated with it, and the US and some small scuffle in 1865.

The real start of transatlantic travel between Italy and the Americas starts in the 1870’s. Why? The Great Depression (not the one in 1929 but 1873). Suffice it to say that cheap wheat being cultivated in the US and Russia put a lot of agricultural laborers at an economic disadvantage and thus many in Southern Europe emigrated to the Americas for metaphorically greener pastures.

To again reference Donna Gabbacia and her work, the destination of Italian immigrants was less connected to where they were from so much as how they were perceived by their destinations. In Argentina (and of course São Paulo-I didn’t forget you Brazil) many Italians were regarded as white Europeans and thus as beneficial additions to those communities because of their supposed “whiteness”.

In the United States Southern Europeans were regarded as inferior to Western Europeans. In the Dillijgham Commison, the US defined a myriad of groups by their ethnicity for the purpose of limiting supposedly non-white immigration. Italy was divided between North and South according to the Dillingham Commison - a South that was demarcated as high as Genoa (meaning that only Alpine regions of Italy like Turin would be considered Northern Italy) and those from southern Italy were regarded as nonwhites. The report used, among other ethnographic figures, evidence from Cesare Lombroso (1835-1909) an Italian craniologist and criminologist who believed that a southern Italians were less civilized and biologically inferior to northern Italians.

So to return to your point, why did northern Italians not go to the United States? Well, they did. There is tons of evidence of migrants from areas like the Veneto came to the United States, but they were rarely regarded by the United States as distinct from Sicilians or Neapolitans (a distinction that Venetians and Sicilians stateside may have been much more keen to deliberate over).

Did southern Italians come to South America? I have less experience here researching this area but my instinct is that both northerners and southerners traveled there. The main distinction being that Italians in South America, particularly Argentina, could mount themselves in the middle class far more easily than fellow migrants to the United States. This is not to say that more northerners than southerners ended up there, but there is a socioeconomic component to this regionalist one as well.

To offer some musing speculation, Italians in the US likely did not have the same access to their regional identities barring linguistic or cultural distinctions. In the end if the US didn’t care about the difference in Venetians and Sicilians the distinction amongst one another may have blurred over successive generations of immigrants genuinely trying to improve their lot in the late 19th-20th Century. As an example (that is more anecdotal than academic but this is speculation) consider that in many pizzerias in Brooklyn or around Arthur Avenue you can buy what is called a ‘grandma slice’ of pizza. The root of that recipe is ‘sfincione’ a type of focaccia bread that Sicilians would label as completely distinct from pizza, a Neapolitan recipe.

In short, the memory of region for migrants from Italy may be just as connected to how much the states they emigrated to allowed for memory as the regions themselves. In South America because of the legacy of colonialism and slavery, Italians were regarded more positively and thus many were able to preserve a regionalist connection (also those coming from the north would have had more money to secure themselves in the middle class than a Neopolitan peasant migrating to do agricultural labor). In the US the complicated picture of Italian, American, and regional identities was much more complicated by state policy.

TLDR; most Italians moving to the Americas displaced by the Great Depression of 1873 moved to either the US or South America and they came from all over Italy. That said, the lands they moved to allowed very different allowances for distinction and memory of their initial homeland. Involved are a multiplicity of distinctions: white and nonwhite, southern and northern, civilized or uncivilized. It is hard to speak in generalities when all of these factors are at play, but what can be acknowledged is the different responses that these nations had to the many displaced Italians moving there for a better future.

Sources: Primary: The Dillingham Comission Report (1911) (I accessed this on archive.org, not certain if access method is a relevant detail to the subreddit)

Lombroso, Cesare: L’uomo Delinquente (1876-1896) (Editions 1-5 mention distinctions between Southerners and Northerners)

Secondary: Gabaccia, Donna: Italy’s Many Diasporas (2000), also an essay in the collection Are Italians White? titled “Race, Nation, Hyphen” discusses some of these distinctions in regards to North and South America.

Edit: Of course a silly typo that I missed.