Published in 1917, The Rise of David Levinsky gives a fine cultural portrait of the conditions and workings of US immigration in the late 19th and early 20th century. Levinsky was authored by Abraham Cahan, editor of a leading yiddisch-language journal, Forverts.
In the book, David Levinsky -- a poor, orthodox Russian jew -- comes to New York in search of a new life, winding up 25 years later, rich, atheist, single and somewhat unhappy.
The novel's main point of interest is Levinsky's urge to integrate -- integration as: to acquire and master the functional culture of his new country. Consequently a lesson emerges for today's agenda in Europe: perhaps the European countries' incentives should be better structured to assure the creation of that kind of urge.
Incidentally, an immigrant Dane, Jacob A. Riis, was behind the contrasting depiction of the period, namely How The Other Half Lives. This book, and fellow Dane Jacob Holdt's later American Pictures are interesting both for their primary effect -- social illustration and enlightenment -- and for their secondary effect (or reception history) in Europe -- as building blocks in the continued, mesmerizing myth about the 'uncivilization' of the US.
See also this post on the role of culture for functional integration in Europe vs. the States.