"Äy" and "Rheims" are equally acceptable answers to this question (apart from the fact that Rheims is a city and not a town – which does not, IMHO, justify disallowing it).
Champagne is made almost exclusively these days from three grape varieties: Chardonnay, pinot noir, and pinot Meunier. The first of these is principally grown to the south of Épernay; the other two are grown to the south of Reims.
There are several other towns and villages where Champagne is produced: for example Mardeuil and Vertus. According to Wikipedia, Vertus is the second largest village in Champagne "one of the highest rated Premier Cru villages of Champagne."
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