I googled to see what a Connector Play Mat is, and those are so cute! I think you could quilt this any way you wanted and it would look good. I personally would go for something simple, as whoever is playing on it won't care how it is quilted. I would just go with straight lines horizontally and vertically....but then I like straight lines. Not everyone does.
Welcome to the board, by the way. I see this is your first post.
Dina