My answer probably falls in the “more information than anyone could possible want to know” category. Nonetheless:
On my mother’s side: my mother’s parents arrived in NYC in June 1941 from their home in Berlin (although my grandmother was originally from a village in the Schwarzwald in Baden), via Lisbon. They were among the last Jews to get out before the borders were entirely closed to Jewish emigration a few months later, and the deportations “to the East” from Berlin began. They had been trying to leave for many years, and were finally able to come to the USA because my grandfather had a first cousin who had already come here with her husband in 1936, and was able to provide the necessary affidavits to vouch for them; the delay was still a number of years. Of course most of what they owned was confiscated, so they arrived with only a few possessions and no money, not speaking the language, and had to start over again in their late 40s/early 50s, working as orderlies at Montefiore Hospital in the Bronx. (When they first arrived, my grandparents stayed with my grandfather’s cousin in an apartment on the same street and block in Washington Heights where I live now, coincidentally.)
My mother left Berlin on Nov. 30, 1938 at the age of 15, a few weeks after Kristallnacht, to go to England on the first Kindertransport. She spent nearly five years there (I posted excerpts from some of her letters to her parents a few years ago), and finally was able to join her parents in NYC in September 1943. She lost two grandparents, seven of her 10 uncles and aunts, and two first cousins (along with innumerable more distant relatives) in the Holocaust. She already spoke English rather well when she arrived in England, and of course was fluent by the time she came to the USA, so she was able soon thereafter to get a scholarship to Sarah Lawrence and then Columbia Law School, where she met my father.
On my father’s mother’s side: my father’s maternal grandparents arrived in NYC in late 1883 with the first six of their nine children; they were from the town of Szczuczyn in northeast Poland, in the Lomza district. They moved upstate to Syracuse, where there was a Jewish community and one of my great-grandmother’s brothers already lived; my great-grandfather had a grocery store/bakery there for the next 40 years or so until his death. My maternal grandmother was born in Syracuse in 1888, and moved to NYC with one of her sisters soon after graduating from Syracuse High School in 1905. (After my father died last year, one of the things I found was my grandmother’s high school diploma.) One of my grandmother’s brothers was actually rather famous in his day as the first Jewish American to win an Olympic gold medal – he won four of them in total, along with a couple of silver medals, in track and field.
On my father’s father’s side: my paternal grandfather arrived in NYC at the age of 15 months with his parents and older sister in July 1888. Their first home was in a tenement building on Suffolk Street that still exists (I’ve taken photos of it). They lived in various other buildings on the Lower East Side until about 1908, when they moved uptown to the Bronx after the IRT was extended up there. My grandfather’s father was a capmaker from the town of Jurbarkas (Yurburg) in the Kaunas district of Lithuania (then part of Russia), and worked in factories on the Lower East Side, dying in his fifties from various maladies probably related to his occupation, forcing my grandfather to leave school at 13 to go to work in the garment industry himself. According to my father, my grandfather’s family stayed in touch with their numerous remaining family members in Jurbarkas until the German invasion of the Soviet Union in late June 1941, but the Germans arrived in Jurbarkas within a day or two, and almost all the Jews in that town (including about 30 or 40 people who were cousins of my grandfather or their children) were murdered.
My grandfather’s mother came from the famous town of Tykocin in northeast Poland (the 17th-century synagogue survives and is now a major tourist attraction – one of my first cousins visited there earlier this year). My grandfather’s parents both emigrated separately to Paris in the early 1880s, and lived in the Marais (then the Jewish slum), where they met. They were married in 1885 and my grandfather was born in 1887. (The very first members of my family to come to the USA were a sister and uncle of my great-grandmother, also from Tykocin, who arrived here in 1879. The uncle is somewhat known in Poland for having been one of the Jews involved in the “January Uprising” of Poles and Lithuanians against Russian rule in 1861; he was probably exiled for some period of time afterwards.)