I've never heard of a major airport in the US where at least the terminal building isn't open at night. And I assure you, HNL is open all night. Those desiring to sleep in the airport just need to be landside. Also, the police may stop by and ask to see a boarding pass or something indicating you're traveling just to prove you're in the airport legitimately.

The only good sized airport I've ever seen close down and kick even overnight travelers out is Perth, Australia.