It’s 4:30 on a weekday afternoon, and you’ve got an hour until boarding starts for your connecting flight home for the holidays. You’re ready for a cocktail. Maybe even two. Which is fine—as long as you’re in the mood to party like it’s 1999. Because, on the whole, airport bars are still running 15 years behind the craft-cocktail movement. In seemingly every American airport, you can find outposts of what might be called the Status Quo Ante Bar, where the spirits are uninteresting and the drinks indifferently made. While dining choices have been steadily improving, and good wine is easier...