Stay strong FreeOwl. Alcohol is a big temptation in Las Vegas, but there are other things to do. You could treat yourself to a few meals at some of the many great restaurants that line the Strip (I'm assuming you're on or near the Strip). Shows are also an option. Personally, I've always enjoyed just walking the strip and checking out the new hotels that had been built in my absence.
Honestly, before I started having problems with alcohol, one of my favorite things to do in LA was to get up early (easy to do since I was on East Coast time), buy a paper, and sit in the hotel's coffee shop restaurant or buffet and eat, drink coffee and read the paper cover to cover.