There is an option (that is set ON by default I believe) to move with the arrow keys. It's a bit tricky to use at first but more precise than the mouse. To move diagonally hit both direction keys at once, it doesn't take up 2 movement points.
If you're like me and use the arrow keys to scroll the map, I usually find the left corner of the square is the best place to click to move. Save often and take your time before moving; I've frequently sent my characters into the middle of battle instead of casting fireball.