Where is "Stay Awake" option in Ice Cream Sandwich on the Galaxy S3?
Samsung removed "Stay Awake" from TouchWiz back in the first OTA for the Galaxy S1. Other ROMs like CyanogenMod still have it, and other AOSP based ROMs as well. 

Be very careful using any kind of "Stay Awake" options with these devices that have the Super AMOLED screens. I used to use it when developing and testing the apps. I now have a "burn" in the screen from the time and the top bar.