Yes, the author, Shirley Jackson, leaves the village, the name of it, the location of it, and anything to do with it in her short story, "The Lottery" vague. We know almost nothing about the village. The only things we know about it are: there are about 300 people who live there, they carry on an annual stoning of one of its citizen, which they call the lottery, and we know some of the names of people who live there.
This begs the question of why Jackson does not give us anything else. I think the main reason is by leaving out details, this village can be anywhere. In other words, as we read, we fill in the details as we imagine what the place is like. This brings the story closer to home, which makes the story erie for the reader.