I had a Sat checkout at the MGM Grand earlier this year. I booked using a "vacations" service that was both airfare and hotel together, and it was a lot cheaper to not stay Sat night, and take the redeye back instead. I checked out in the morning and had the bellman keep my luggage for the day, so I got to stay in Vegas all day on the strip.

Anytime I've been looking at Vegas trips, the pricing has been the best for advance package purchases with air/hotel together. You could also look to Priceline/HotWire to try and get some discount rates.