Proximity from the monster’s current position (i.e. number of hexes they are away, not counting through walls, but counting through everything else) is then checked as a tie-breaker for determining “closest.”
If more than one enemy still ties for being the closest, the second priority is to focus on the enemy who is earlier in the initiative order
Summons are focused on before the character who summoned them in this regard, even on the round they are summoned, and a character who is performing a long rest would be focused on last.
Example: Even though the Brute is physically closer to Monster , the monster is performing a melee attack and can get in range of the Tinkerer in fewer steps (2 instead of 4), so the monster focuses on the Tinkerer .
In the case where there are no valid targets on which to focus, because there are no valid hexes a monster can attack from (i.e., they are all blocked, occupied, or there is no open path to reach them), regardless of the number of hexes it could move, a monster will not move or attack on its turn, but it will perform any of the other actions on its ability card that it is able.
Treat traps and hazardous terrain that would be triggered by the move as obstacles unless they are the ONLY open path towards the destination hex.
Monsters will minimize the number of triggered negative hexes. See Monster Movement: Traps/Hazards.
Ignore traps, hazardous terrain, and obstacles when determining focus if the monster has Flying or Jumping. As the monster can move over these without penalty.