Mayflower ancestors, and most of the family has been here since before the American Revolution. I had one G-G-Grandfather come over from Denmark in the 1800s, and my grandmother’s parents were immigrants from Ireland around the turn of the century.
Ours was with what generation Mormon you are. Which for most of the LDS families coincided with what generation (minus one) American you were. Lots of Scandinavian immigrants, with a few English and one French thrown in for “cross-culture” ancestry. My father’s father’s father’s father’s line goes back pre-Civil War as well as a few others who also joined the church in its early days.
Now I’m the immigrant and not Mormon. Go figure.
All my grandparents were born in Japan, but I am the rare second generation Californian.
My niece is 7th generation Californian.
On my father’s side, my great grandparents came from Prussia in about 1840. On my mother’s side, all the family lines go back to colonial America, including Mayflower travelers.
Family tradition says 7 of my great grand parents were born in the US, and it’s probably true though I haven’t tracked down each one. On my mother’s side it’s celebrated that one of her grandmothers immigrated from England, though also Irish Catholic as is every other known branch of the family. I was able to track that down on an ancestry site and sure enough she arrived in NY in 1867 at the age of 2, from England.
There’s said to be an ancestor along my dad’s line who lived in Charleston by 1830. At least one other branch on his side had some people there at one time, but all the more recent generations lived in NY or more specifically (and a separate city back then) Brooklyn, which is really the ancestral family homeland more than Ireland itself. Even my grandparents’ generation didn’t know specifically of any relatives in Ireland. My 16 g-g-g’s though were probably mainly immigrants from Ireland.
Both sides landed in the late 1600s, early 1700s. The first on either side to venture out of New England was in the 1980s, and he was only one of a handful who has to this day. Our roots are taproots. 
My Mother was Canadian, but she has some direct ancestors that were born in Colonial America and fought in the Revolutionary War.
I got records that has traced her ancestors to the early 1700’s along the Hudson River.
Actually both my parents have ancestors that date back to Colonial America but some generations immigrated back and forth.
My fathers ancestors were loyalists and that is why they moved to Canada after the Revolutionary War.
My ancestors, the Wyckoffs, built the oldest building still standing in NYC, it’s in Brooklyn and is a historical monument.
All of my grandparents were born in the USA, but at least three great-grandparents were immigrants. My father’s father’s father (ethnically Bohemian) was born in a part of Austria-Hungary that is currently Romanian. Father’s mother’s mother came from what’s now the Czech Republic – she actually made the crossing a few times, and two of her children were named Frank and Frances partly because they were born in France.
Mother’s mother’s mother was shipped from Germany to America as an orphan child to become a servant girl for a Baltimore family. Although she was raised Christian, she may have been of Ashkenazic heritage, as her surname is fairly common among both Jews and gentiles.
One of my grandparent forebears is John Howland, the guy who fell off the Mayflower. Other family were Irish-Scots mongrels who dribbled over in late 185th c. Mom claims we’re direct descendents of Wm the Conqueror (zealous Mormon geneaologist - take with large grain of salt).
My matrilineal grandparents came from Rotterdam in 1918. My blended surname would be something like MacVanDougallVonEkker:D
I’m the same way. My ancestors left Europe in the 17th century and didn’t come to the United States until the 20th century. (In our case, the prolonged stopover was in Quebec not Central America.)
That’s my father’s side. On my mother’s side, we’re an old New England family going back to pre-Revolutionary times. One of my ancestors was one of the founders of Hartford, Connecticut. There’s a street named after him.
My mother & grandmother were born in Fort Worth, and my great-grandmother and great-grandfather were born in Texas.
So I’m a fourth generation Texan, at least. I’ve not really gotten back farther than that, but there’s at least a couple or three more generations of U. S. births, I’m sure.
I’m a direct descendant of Anne Lucy Howard, of the powerful Howard Taft family. My maternal side goes back to the founders of Massachusetts.