Amazon offers Call of Duty: Advanced Warfare for PlayStation 4 or Xbox 360 for $39.99 with free shipping. (It's also at this price for PlayStation 3 but temporarily out of stock. Meanwhile, GameStop charges the same for various platforms.) That's the lowest total price we could find by $10, although we saw the Xbox One version for $10 less four days ago (since expired).
Orders placed by December 19 should arrive by Christmas; that deadline is December 22 for Prime 2-Day Shipping. (Note, however, that the Xbox 360 version won't be in stock until December 23.)