GeoElevationData has several new options in version 12.0, with GeoRange and GeoRangePadding among them.
In versions 11.x, a possible way to obtain a geo elevation matrix for a region or radius r around point p is to use GeoDisk[p, r]:
GeoElevationData[GeoDisk[IslandData["Corsica"], Quantity[200, "Kilometers"]]]
