What are you looking for in a community? A couple of places come to mind, though they may not be as exclusively Italian as they used to be, but the Little Italies of Endicott(a bigger/company town village west of Binghamton, whose Little Italy is on the North Side/End of the village:
Little Italy Endicott - Now that's Italian! ) and Rome, which is centered around East Dominick Street on the city’s East Side. It is about 15-20 minutes west of Utica, another city known for its Italian population, which has historically been centered on the East Side of that city. Utica has a current history of people of Italian descent in government(the mayor, most of the city council, etc.).
A few other communities that also come to mind are Lyncourt(a small place in the town of Salina north of Syracuse), Solvay(a company town village west of Syracuse known for its Tyrolean/Italian population) and Frankfort(a small town east of Utica). All have some of the highest percentages of people of Italian descent.
Other places that come to mind is Auburn’s West Side on both sides of the Route 5/20 arterial road; Cartland around St. Anthony’s of Padua church, parts of the North Side(and still the West Side to a lesser degree) of Buffalo, western Gates(a western suburb of Rochester), North Syracuse(a village north of Syracuse with quite a few Italian restaurants/bakeries), the Breen Street area of Watertown, the South Side of Amsterdam, Seneca Falls, Rotterdam west of Schenectady(due to some moving out from the Mont Pleasant neighborhood of Schenectady, which also has a Little Italy business district off of Union Street), parts of the North Side of Syracuse(still has businesses in the inner portion closer to Downtown, but many still in the city live in outer neighborhoods closer to Lyncourt like Court-Woodlawn north of Grant Boulevard or even around Sedgwick) or even the Eastwood neighborhood, parts of Troy south of it’s Downtown(which was/is marketed as its Little Italy:
https://m.facebook.com/113776213346664/ ), East Rochester(a village east of the city), parts of Greece and Irondequoit (suburbs of Rochester), some small communities around Mount Morris in Livingston County, the Pine Street area of Niagara Falls(still marketed as its Little Italy, though more mixed with north of the street still having a good sized Italian presence), Canastota in between Syracuse & Utica and more.