Create a Mesh Region from Geographic Data 

Using VoronoiMesh, divide the area around Italy into cells that represent the regions closest to each major city.

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X coords = Table[ Reverse[CityData[c, "Coordinates"]], {c, CityData[{Large, "Italy"}]}];

Generate Voronoi mesh from city coordinates.

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X vm = VoronoiMesh[coords]

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The closest city at any point is the one contained in the corresponding cell.

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X Graphics[{Lighter@Brown, CountryData["Italy", "Polygon"], PointSize[Medium], Red, Point /@ coords, Thin, Black, MeshPrimitives[vm, 1]}]

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