"an incorporated municipal unit in some states (as New York) having a separate status and some independent powers although still constituting part of the parent town (a thickly settled area in a town, faced with some problems of living close together, may be incorporated into a village Our State & Local Gov't of New York)"

So the question seems to be whether or not the village in question is officially part of a city or town, and if so which one.

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Note added at 10 mins (2005-01-18 14:53:00 GMT)
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sorry, title line should read \"Webster\'s definition of village\"

Die Stadt

English makes a distinction between city and town that German does not. Therefore in most cases I would use Stadt for both city and town. Big metropolitan areas or big cities like New York are often made up of towns: There is Manhattan, Queens, etc.. So it depends on the context.
In the first field:
city of
town of + name
village of

In German I would say
Stadt Name:
Dorf Name:

Second field:
Rural areas often belongs to municipalities or similar administrative sections. You might have a house outside of the city limits but that area is administrated by a town nearby and you pay your property taxes there. I am not sure about the German term maybe Gemeinde or Dorf. Good luck.

Das wäre eine weitere Möglichkeit. Wenn sich City, wie in dem Beispiel New York, in Towns wie Brooklyn, Queens, Manhattan usw aufgliedert, das wäre dann vergleichbar mit der Stadt Berlin, wo jeder Bezirk wie Charlottenburg, Schöneberg, Lichtenberg, Kreuzberg,Weißensee usw. seine eigene Stadtverwaltung hat.