I just did this Monday night with Hertz.
We stayed at the Sheraton Gateway and dropped off our car in the evening so we wouldn't have to do it on Tuesday morning before our flight back home.
I took the Hertz shuttle back to the airport and then the hotel shuttle back to the hotel. It took about 1 1/2 hours to do all this, but then the airport was jammed and our hotel driver had to make a couple of other stops to pickup more folks going to the hotel. I was able to save about $25 by dropping if off a day earlier.
As to what you may be saving depends on when you picked the car up.
The car companies use 24-hour cycles for their billing. In other words, for example, we picked up our car at about 8:30pm and by dropping our car off about that same time, we were able to save the $25. If we had waited 2 or more hours later, we would have been charged the extra day.
Another thing, as Karylrocks said, is to check if by dropping your car off a day early, would that invalidate a weekly rental rate(if that's what your rate is). The best thing would be to call Alamo and ask them how that would change your rate, if at all.