The earliest I was able to get a room in Sheraton LGA is about 12pm, if you don't mind your bed preference. Again, I never try anything earlier. Once , I was told to come back at checkin time when I showed up at 2pm. So, you may get lucky if the hotel is not full the night before. I believe SPG Plat will give you a slight edge.
As a gold, I always got lounge access there (but the lounge is nothing to write home about).