I'm not sure what the number is - I've never been a situation where it was actually going to take anything close to $500 to get a random airport hotel. One-night airport hotel stays are often a pretty decent use for points, which is what I've typically done when this has happened to me. A couple other times the hotels have been cheap enough that it wasn't a good use of points - like $100-125 for a Fairfield-quality place.

The only time I've decided to remain in the airport overnight was when I had been rebooked (confirmed) on a 5:15AM flight. I didn't trust the hotel shuttle would run at 4am and this was pre-Uber. It was already midnight so I just chilled in the airport and didn't sleep. Yeah, the next day sucked, but I didn't want to chance no-showing my confirmed seat.

I thankfully have never been caught up in one of the mega-storms that causes a whole city's hotels to be sold out. I guess in that case I'd just find a quiet corner of the airport and chill.