Just sleep in an airport. This site has tips and reviews of places to sleep in many of the world’s airports, plus general airport sleeping tips. I know I’ve had to sleep for a few hours at the Minneapolis, Denver, and Portland airports (due to weather delays), and Portland was by far the nicest. Denver wasn’t bad (as it was just rebuilt), and I was one of the lucky few who found the benches at the Minneapolis airport.
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I fortunately have relatives conveniently placed near major airports – Manchester (UK), Minneapolis (US) and Bridgetown (Barbados) :).