Does "new city" mean a city no other players are infecting?
A new city means one that you are currently not infecting.

From the infect a city infection rules,


  You can infect a new city OR a city you are currently infecting.
  
  new city: Discard 2 cards whose color must match the city you
  wish to infect. Place your disease cube(s) on the uppermost
  available row (without any cubes).
  
  City you are currently infecting: Discard 1 card whose color must
  match the city you are currently infecting. Place your disease
  cube(s) next to those already on the City card.