When Does "Hamilton" (2015) Take Place?
"Hamilton: An American Musical" is a historical fiction opera written by Lin-Manuel Miranda first performed February 17th, 2015. So when is "Hamilton" set?
It takes place in the years:
We know this because the second song "Aaron Burr, Sir" opens with the words "1776 / New York City." and the real-world Alexander Hamilton (1757-1804) implies that he was just "at Princeton. I was seeking an accelerated course of study"... (Though, in the real world, Hamilton first applied to the College of New Jersey [which, after 1896 AD, became Princeton University] in 1773 AD.)

1776 AD - 1804 AD
We know this because the second song "Aaron Burr, Sir" opens with the words "1776 / New York City." and the real-world Alexander Hamilton (1757-1804) implies that he was just "at Princeton. I was seeking an accelerated course of study"... (Though, in the real world, Hamilton first applied to the College of New Jersey [which, after 1896 AD, became Princeton University] in 1773 AD.)
Later, "The World Was Wide Enough" the second-to-last song, depicts the famous and tragic Burr-Hamilton duel, which happened on July 11th, 1804 AD in the real world. So it's certainly July of 1804 AD.
Additionally, the first song "Alexander Hamilton" functions as a musical overture and a narrative prologue quickly covering the real-world Hamilton's biographical details from his birth ("The ten-dollar Founding Father without a father") in 1757 AD to being sent to New York ("In New York you can be a new man") in 1772 AD.
This website examines its exact setting.