when a hero moves 1 tile do they just move into any square they want?
I assume you mean that the Hero moves due to something external such as an Event card or being attacked by something like a Feral Troll (who can cause 3 Damage and moves the Hero 2 tiles).
If I remember, the rules or FAQ do not cover this but the general consensus is that the Hero is placed on any vacant space on the tile.
EDIT: BTW, the LoD FAQ has this to say.
Where do I put a Monster that I move with one of my Powers or
You can place the Monster in any unoccupied square that meets the
effect’s requirements. For example, Tide of Iron allows you to place
the Monster on any unoccupied square on any tile within 1 tile of
your Hero’s current location.
While this doesn't cover what to do with Heroes, it's not much of a stretch to apply the same logic.