Several things are said in the opening pages of “Rip Van Winkle” to let you know where the story was set, and when it was set, which is part of where it was set, in this story. The first statement is the first line of the story: “THE FOLLOWING tale was found among the papers of the late Diedrich Knickerbocker, an old gentleman of New York, who was very curious in the Dutch history of the province, and the manners of the descendants from its primitive settlers.” This does not guarantee that the story will be set in New York during the period when the Dutch owned it, but it suggests this is likely.
This suggestion is reinforced by this line, found just a bit later in the story: “The result of all these researches was a history of the province during the reign of the Dutch governors, which he published some years since.”
In other words, after he researched this region of the period, he wrote a history of it. That still doesn’t guarantee the setting, but it makes it more likely.
This setting is confirmed just a bit later, in this line: “Whoever has made a voyage up the Hudson must remember the Catskill Mountains.”
Geographically, our setting is confirmed. Even if it was New Amsterdam at the time, it is what we call New York.