Due to the diversity of Indigenous communities across on the eastern half of North America during the late Colonial Era era, generalizations about their experiences will fail to capture the complexity of their lived experiences. That said, there are a few patterns we can look to that can shed some light on your question.

First, it was not uncommon for Indigenous people to live their normal lives in or near white-dominated communities and cities, without attempting to pass for white. In this response to a previous question, In late Colonial America, how often did American Indians visit (or reside in) colonial urban areas?, I get into some of the native communities that could be found around New England and their interactions with white education systems.

In other words, many Indigenous or Native people born on East Coast remained on the East Coast and their experiences included marrying into white families and raising their children in their new communities as well as living their entire lives surrounded by members of their clan, maintaining the traditions and culture of their ancestors. There are currently ten tribal reservations or sovereign nations inside the boundaries of New York State, some of them dating back to treaties signed in the late 1700's. Additionally, there were numerous Native men who played a role in the Revolutionary War and the War of 1812. One such example is Governor Blacksnake, also known as Tah-won-ne-ahs or Thaonawyuthe. He fought on the side of the British during the Revolutionary War and was a leader in the Seneca Nation, which covers a large portion of New York State and played an important role in negotiating the nation's boundaries.

Your question mentioned the possibility of living as a US citizen and to clarify, the issue of citizenship for Native people wasn't resolved until 1924 and the passage of the Indian Citizenship Act, as the 14th Amendment ("All persons born or naturalized in the United States, and subject to the jurisdiction thereof...") wasn't applied to most Native Americans. [There is also an argument to be made that the issue wasn't resolved until the Civil Rights Act of 1964, but I'll defer to others on that issue.]