Mover

public class CharacterMover : MonoBehaviour {

    // Where we want our character to go
    private Vector2 destination;
    // How fast we want our character to move
    public float speed;

    void Awake () {
        // Sets the destination to the current postion at the start
        destination.x = this.gameObject.transform.position.x;
        destination.y = this.gameObject.transform.position.y;
    }

    void Update () {
        // If the user holds down directional input, the destination changes by 1 in the proper direction
        if (Input.GetKeyDown("down")) destination.y = destination.y - 1;
        if (Input.GetKeyDown("up")) destination.y = destination.y + 1;
        if (Input.GetKeyDown("left")) destination.x = destination.x - 1;
        if (Input.GetKeyDown("right")) destination.x = destination.x + 1;

        // If the destination isn't at the postion, move towards the postion
        if (this.gameObject.transform.position != new Vector3(destination.x, destination.y, 0)) {
            // Code to move towards the destination by the speed
        }
    }

}