movement in a tactical game - need advice

I'm trying to make a strategy game - I'm converting Zombie Plague (do a google search) from a miniatures board game into a video game. I am trying to figure out the best way to have them move around the board. The board is a grid like a checker board. I am trying to figure out the simplest way to move the characters to the center of each square. I can't count on the board squares being drawn perfect, so simply incrementing the character's x or y positions by a set amount will result in the character getting further and further away from the centers of each successive square. I'm kicking around the idea of having an actor at the center of each square to somehow mark the positions the characters are to move to. I just don't know how to get the characters to go to the appropriate marker actor. Anybody have any suggestions?