If your sentence was "the cat sits/stands/lies at the bottom of the stairs," it would make a difference. With "village" as the subject, it really doesn't matter -- you can use any of the three, with no real difference in meaning. "Stands" seems a little less likely than the other two and "lies" would probably be the most common.
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khoff "lies" would probably be the most common.And I think it is the more graceful, as well.