Old stock New Yorkers

[Coney]

I don't think you can compare New York with London or Paris in that way. First of all, New York is a much newer city. The original inhabitants, the tribes of Manhattan, Brooklyn, Queens, Staten Island are basically extinct. There are still Native American tribes living on Long Island and upstate New York. The Dutch were the first Europeans to develop a settlement with their African slaves, although not the first to come sniffing around the area. After the Dutch, the English took over without firing a shot. The Germans and the Irish came much, much later.
We still have our "bluebloods" living here, the Vanderbilts, the Astors, the Roosevelts, the Van Wycks, descendants of the British Isles and New Amsterdam, but there is no specific neighborhood for them. If they are still linked to the family money, then they may have an apartment in the rich part of Manhattan as one of their residences. In Europe, people can trace their link to aristocractic roots back 500 years. We can't do that here unless it can be traced back to "the old country" and remember, there never was a "ruling class" or nobility like there is in Europe. In Europe, the landowners were the upper class. Here, plenty of poor land owners. That was a big selling point of coming to America. Anyone could come here and become a landowner. You didn't have to inherit property. You could get many of acres of land for free through the government homestead act.

[King of Kensington]

By the late 1800's there were few white American Protestant working class New Yorkers left - they had moved up economically or left the city. Those that remained tended to be middle and upper class. Only 18% of the city's population in 1890 (after the 19th century Irish and German waves) was made up of native whites of native parentage (i.e. at least third generation American) and that number barely budged to 22% in 1930 (after the great migration of Eastern European Jews and Italians). It seems reasonable to assume that probably 50% of that 22% in 1930 would have been the grandchildren and great-grandchildren of Irish and German immigrants, and when you include other descendants of 19th century immigrants etc., the colonial stock white Protestants would have been no more than 10% (and as nei points out, they were estimated to be about 5 percent of the population in 1960).

[Kefir King]

"Old stock Americans" weren't white.

[King of Kensington]

The closest NYC equivalent to London cockney is probably the "New York Irish" accent of Archie Bunker.

Many London Irish and Jews also spoke with the Cockney accent, given their residence in the East End.