Having worked in a large office building in Los Angeles--the tallest one, actually--I find it strange that, even on Christmas Eve, the Nakatomi Plaza is empty of people except for that one party. (Nevermind that the guy at the front desk is a bit of a jerk for directing John to the computer rather than just saying, if your wife is here, she's on 30.)
I worked for a law firm that had a documents department that worked 24/7 and case closings--with a whole lot paperwork--happened through the night. I once did a temporary shift on a closing that ended at 6am. Big office buildings in, well, any large city--they just are never empty. Hell, Die Hard depends on the big business of the 1980s, from the limo service to the eurotrash "terrorists" to the whole Holly-moves-to-Los Angeles angle.
(An aside, I just noticed in the opening credits that the director of photography was Jan de Bont. I'm not surprised. There are more than a few shots in this movie that have an obvious artistry to them. De Bont served as DOP on, among other things, Cujo and would eventually direct Speed.)
Christmas may close down some grocery stores. And, local shops may close. But, big offices--those things just do not close, especially in the world of multinational corporations like Naktomi. Business even before the 80s was a constant thing. By the late 80s, business was... it was always, it was everywhere.
Separate thing: Since I've suggested that 80s actions movies were essentially a response to the Vietnam War, one must ask how Die Hard responds to the Vietnam War. It's interestin because, at first, this film just doesn't. But then the FBI guys get their helicopterss and fly in like they're flying down a river valley in Rambo... but, they fail. So, maybe this movie marks a sort of ending to the this time we win cinema. Maybe, finally, the Vietnam War was over here in Die Hard