Imagine mach-6+ flights carrying 20K passengers at a time going NYC --> South Asia within an hour or two. Entire town populations commuting to a diffefent continent every day!
But I am forced to admit that airborne aircraft carriers like in Sky Captain would be very cool. (I guess some people like to call those "helicarriers", but I can't get past the busted etymology.)
A helicopter or balloon with an unshielded nuke reactor hanging below it, that never needs to land, seems pretty cool.
More seriously, if you want to learn more about the history of aircraft nuclear propulsion research, the HTRE reactivity excursion report contains quite a bit of design overview in it as background for the rest of the report.
[1] https://en.wikipedia.org/wiki/Roll-on/roll-off ferry?
Make it more cylindrical, and have hyperloops disgorge their metro cars into them like bullets into the magazine of a revolver. Have a dozen of such magazines behind each other, or so.
Lift off, travel, arrive, disgorge into local Teslatronic Transglobal Transportation Trix branch network. Next best thing to 'beaming'.
Use the electric power of the [1] https://en.wikipedia.org/wiki/Nuclear_lightbulb for propulsion like this:
And why bother with batteries when there are