Can I choose not to move a unit with something like Ride the Wind or Charm (for example, to keep it in the same spot)?

No, you cannot choose not to move a unit if you play a spell like Ride the Wind or Charm.

When you play a spell that includes an instruction to "move a unit," that move is a mandatory part of the spell's resolution. According to Rule 356.3.e.11, instructions that can be followed must be followed. Because "moving" a unit is an action the game can perform, you must execute the move if a valid destination exists.

Furthermore, Rule 425 defines moving by its Origin and Destination. If you play a card that instructs you to move a unit, you must select a valid destination for that unit. You cannot choose to "move" it to its current location to effectively keep it there, as a move requires a change in position (Rule 424.1).

If there are no valid destinations available for the unit (for example, if all potential destinations are invalid due to game state restrictions like those in Rule 425.2.a), the instruction to move would be ignored as per Rule 356.3.e.6, but you cannot voluntarily choose to ignore the instruction if a valid move is possible.