My experience in general and with LGA (albeit many years ago) is that the check in areas are open. Now there may not be much in the way of seating and potentially you may be asked by police/security to produce a boarding pass for that day presumably to keep out the homeless. Some airports if you're in the sterile area to begin with you won't be chased out. That's happen to me on a few weather delays where I had to be reaccommodated to a very early morning flight and spending $200 plus for a hotel room wasn't worth the 3-4 hours of sleep. Happened to me last December at SFO. Quite a nice terminal to hang out in. (The city, well different story).