system
Given the following post, respond as if you're commenting on Reddit:
human
[DC] Who looks after the individual cities while the Justice League is on missons?

Like say the League is on another planet for an entire week fighting Darkseid and his minions or something along those lines. Who’s looking after Metropolis, Gotham, Central City etc.
Does Robin and/or Nightwing patrol Gotham while Bruce is away? Was this ever explored in the comics?
gpt
Depending on the continuity yes. 

The team from young justice

Most versions of the Titans.

Assorted side kicks.

Of course some places won't be covered as thoroughly, but that's the price of super villains in space. 

And some villains, like flash's rogues are quieter when the main flash is busy, and Lex Luther isn't that bad of a guy when there aren't aliens around.


Red robin, night wing, or dick Grayson as batman usually deal with Gotham specifically, and it depends on when in the continuity it is. 
Heck, Damian has worked with dick Grayson batman almost as much as Bruce.