I always go to this liquor store the moment I land in Vegas. They have comparable prices to every liquor store on the strip and it's so convenient because it's right next to the baggage claim area.
Also, every time I've stopped in there, they're always giving away free alcohol. And if you buy something that's warm (lets say you grab a warm 24 pack of beer) the employees always ask if you want it cold and even offer to go get it for you so you can have cold beer over warm beer.
This place is a must-stop-at place once you arrive in Vegas.
Enjoy!