You can play LAN games with a set of Xbox 360's, this is called System Link. The system link support varies per-game though. Co-Optimus confirms that you can play up to 2 players per system on 2 systems, and this can be done in either Zombies or Multiplayer Mode.
I've personally played Modern Warfare 2 on a LAN with about 12 Xbox 360s. Call of Duty games through Modern Warfare 2 supported one player per 360; Black Ops and Modern Warfare 3 allow 2 players per 360.
If you really want to play system link games, I'd suggest picking up Halo: Reach or Halo 3, as both of those games support 4 players per console, up to 16 players in a game total if you have 4 Xbox 360s. You can also consult Co-Optimus, or this list of system link games on Wikipedia. (The list contains an error: COD Ghosts does not allow 2 per console.)