Las Vegas is already a true 24/7 city. There are a zillion people gambling, drinking, dining, etc. overnight, of course. But Las Vegas also has the nation's highest percentage (
16.54%) of night-shift workers, who keep that party rolling. New Orleans has overnight drinking as well, but its nightlife is less diverse and is at a much smaller scale.
After those two, I suppose Chicago comes closest with its late closing times, especially on weekends, but it's technically not 24/7 and I haven't seen any indication it will go all the way.
Forget about Boston. Even in the decades when nightlife was more popular than it is now, Beantown still closed down early. And the California cities all have 2:00 a.m. closing times. You can party all night in Los Angeles,
even on weeknights, but only if you already know where to go--so that doesn't really count. San Francisco used to have a rocking nightlife scene but that died out slowly over the last 30 years or so, and the trend seems to be earlier and earlier closing times.