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.
Shirley Jackson could not have named a real town because her story would have been libelous. She would have been accusing the inhabitants of committing seventy-six murders over the past seventy-six years. And they could easily prove that no such lottery had ever existed in their peaceful little community . The alternative would have been to make up a name and place the fictitious town in a real state. But then the people in that state would be in an uproar, denying that any such lottery had ever existed there. Furthermore, the narrator mentions other nearby towns where there used to be lotteries and other neighboring towns where the lotteries still exist but the residents are thinking of abandoning them. If she even mentioned a real state, such as Nebraska or Iowa, she would appear to be suggesting that the entire state was covered with small towns where the people engaged in ritualized murders. So Jackson could not name a real town or a real state. It would seem to be malicious libel if she did. The alternative was to let the story take place in a sort of Never-Never Land. I think the reader knows that this lottery is not real but allegorical. Therefore it is right that it should be taking place in such a Never-Never Land like the strange setting of "The Country of the Blind" by H. G. Wells.