Once I read that, and realized I didn't know the answer right off the bat, I knew the gauntlet was thrown down. No Google, I'm quarantining myself from outside sources and I'm going to list all of the First Ladies I know and try to guess.
- Martha Washington, from an aristocratic planting family in Virginia. Probably was born there too.
- Abigail Adams
- Thomas Jefferson had no First Lady.
- Dolly Madison
- What was Monroe's wife's name... I have not a clue.
The Founding Fathers' wives were, IIRC, all American citizens at the time of the Constitution's signing. I'm excluding 1-5.
- JQ Adams's wife, I could see possibly being foreign-born. He was very erudite and well-traveled. I know that he was the Minister to Russia, and he might have also been minister to other countries. His son Charles Francis Adams was the US ambassador to the UK during the Civil War, during which he kept the UK's position effectively neutral with extraordinary finesse.
- Rachel Jackson was almost surely a homespun American woman, Old Hickory likes them that way only. Her untimely demise was a tragedy for the incoming President.
- Van Buren's wife was probably American. I do not know anything about her though.
- WH Harrison's wife... no clue.
- John Tyler, I believe, had more than one wife. Probably from Virginia like him. He was very prolific in making children too, producing his last child in his 70s. There are still living grandchildren of President Tyler, a man who was born in the 18th century, because apparently Tyler family males never stop making babies until they die.
- James Knox Polk was from TN or KY. Unlikely.
- Zachary Taylor was, I believe, a Virginian. Unlikely that his wife was foreign.
- Fillmore? For some reason this seems possible to me.
- Franklin Pierce, I did remember reading about his family life. Apparently he and his wife were both witness to their son dying in a train accident, which traumatized them both and contributed to his indecisiveness as president. I do not recall his wife being foreign-born, so I am doubtful that she was.
- James Buchanan, "Old Public Functionary," was famous as a bachelor. Some historians believe he was gay, but I'm uncertain.
- Mary Todd Lincoln was definitely not foreign-born, she was from an aristocratic slaveholding family, from Kentucky I think.
- Andrew Johnson from Tennessee probably didn't have a foreign-born wife.
- Julia Grant was not foreign-born. I'm unsure of her family background, but she and US Grant did put up with a lot when he was struggling between the wars to find steady work.
- Lucy Hayes (I remember her name because she was a temperance advocate, and called "Lemonade Lucy" because she refused to serve alcohol in the White House) was American-born.
- James Garfield's wife, I am not sure. Garfield was one of the least wealthy men to become president, was a minister and officer and teacher, and so as an eclectic man of his time may have wed a foreign-born immigrant to the United States.
- Chester Arthur's wife, I know nothing of her. President Arthur was apparently very productive during working hours but never worked late, so he probably enjoyed spending time with her.
- Grover Cleveland admitted to fathering an illegitimate child, but was his wife foreign-born? I seem to remember he was married in the White House and she was younger than him and maybe she is the one.
- Benjamin Harrison, from Indiana, probably not his wife.
- McKinley of Ohio, not him.
- TR's wife, why do I know nothing of her? I've read the man's autobiography and he barely talks about anyone but himself.
- Taft's wife (maybe named Helen) was probably born in Ohio like him.
- Woodrow Wilson's wife, whose name I believe was Edith, was a very important First Lady because she effectively took control of the US government in the wake of Woodrow's stroke. You go, girl!
- Warren Harding's wife... probably not.
- Calvin Coolidge's wife, no way.
- Herbert Hoover's wife... I do not know either way, but for some reason I'm going to say possibly.
It gets much easier with post-WWII presidencies.
- Eleanor Roosevelt was American-born, I am fairly sure.
- Bess Truman was, like Harry, a native of Missouri.
- Mamie Eisenhower was, I believe, also American-born. I have read some of Ike's autobiography, but I found it pretty dry.
- Jacqueline Kennedy was American-born.
- Lady Bird Johnson was definitely a Texan.
- Pat Nixon was definitely American.
- Betty Ford, no.
- Oh crap, I don't know Jimmy Carter's wife's name! Sorry. But I imagine you're from Georgia like him.
- Nancy Reagan, no.
- Barbara Bush, no.
- Hillary Clinton... I think we know a little bit about her than most First Ladies.
- Laura Bush, no.
- Michelle Obama... for some reason I don't know where she is from, but I'm almost certain it's US.
So having listed all of them, I have to narrow down to one guess. My shortlist of possibles is Cleveland, Garfield, Quincy Adams, TR, Hoover.
Beyond that I have no clue, but I tried my best. I'm going to guess John Quincy Adams's wife (not sure on the name), because I know that he had a deep tie to Great Britain, his son ended up as the ambassador to Britain, so maybe she was British.
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Checking Google... holy crap, I was right (except I didn't know her name)! The first foreign-born First Lady was Louisa Adams (1776-1852) who wed John Quincy Adams in 1797, when his father was second President of the United States. John Adams was at first hesitant to having a foreign-born daughter-in-law, but eventually he warmed to her. She was unfortunately in ill health frequently, had many miscarriages, and was depressed during her time in the White House.
Corrections after the fact-
- Rosalynn Carter. Duh.
- Rachel Jackson was actually never First Lady, since she died before he was inaugurated. Jackson had two First Ladies in office.
- Woodrow Wilson did have a First Lady named Edith who was the one I remembered, but his first wife Ellen died in 1914 with him in office. He married Edith in 1915.
- Like Wilson, Cleveland also married in office, and she was a good deal younger than him.
- James Monroe's wife was Elizabeth.
- Dolley Madison is the name of James Madison's First Lady. Pardon my spelling; I seem to have been confused by the existence of Dolly Madison baked goods!