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Most half bottles of Champagne cost closer to two-thirds the price of a full bottle than to half, so it's usually hard to save much money with that approach. But since you're in New York, you might try PJ Wine (way up Broadway in the 200s), which has halves of Veuve Yellow Label for $13, which is a very good price (if you live Veuve).

I don't think you'll find any actual Champagne for much cheaper than that per half bottle, as most of the smaller houses whose wines are better values don't bottle anything smaller than standard.

If you're willing to consider bubblies from outside Champagne, you might have more options.

Eric