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I would worldize explosions and animal roars and other transient effects from my library under a freeway overpass or other echoey bridge or tunnel or acoustically odd public space where there isn't much people traffic that day. Large concrete spaces = lots of 40 Hz and below !!!
I would also get Subway stop idents (when the conductor or computer voice says "Next Stop.. Hollywood Blv." etc. and I would also seek out traffic pedestrian crossing signals (the beeps and notifications for the blind to cross a city intersection) Those are very difficult to come by a really clean recording of and I would imagine they would be valuable to people who do films in city environments.
If Dallas is quiet enough and you bump up your gain loads then you might just be able to pick up the faint sound of sleigh bells as Santa makes his way back to Greenland after a long and hard night's work.
Failing that, it's all about the urban slap acoustics really isn't it?: shouts, exterior doors, distant sirens.....the usual suspects that are normally swamped by the fog of noise that is modern city life.
Only other thought is interior public spaces which are normally overrun with people: ticket barriers, ventilation units or escalators on the subway, perhaps?
I'm going to be in the woods, so I'll probably record some ambiences. If I were in the city though, and it were as quiet as you're suggesting, I'd go out and try to get stuff that would otherwise be mangled by traffic noise.
Are there crosswalks that have those audible indicators for crossing? Those might be useful when building ambiences. Can't think of any other examples at the moment, but I'll edit this if I do.