Take for instance the Chinese. In Manhattan you could hear a lot of people who speak Cantonese, Mandarin or another Chinese dialect - and not just in Chinatown. There are plenty of laundry shops and convenience stores operated by the busy Chinese who usually prefer to speak the language of their ancestors. When I am there I get the feeling having jumped around the globe.
This also applies for Spanish. I hear this language very often in the (budget) gym I have been visiting or in plenty of the bodegas (small groceries) in my neighborhood. Many official anouncements, for instance in the subway, are written in 2 languages, English & Spanish, catering the uge part of the US population coming from Puerto Rico, Mexico and other Latin American countries.
Other ethnic groups, like Indian, Ukrainian or Russian, are nursing their cultural identity too.
I believe that the diversity of cultures is one of the most valuable assets of the metropolis. The assortment of different ethnic populations gives New York even more life. It´s entertaining and you could learn a lot from the variety of foreign cultures.
Part of the advantage is the spectrum of restaurants which serve Chinese, Japanese, Indian, Ukrainian and other ethnic focused cuisines. Variety is the spice of life and the kick of New York City.