I know organized play dates are great for busy moms, but there's also something nice about the kid next door yelling over the fence, "Can Judy come out to play?" There's a lot to be said for two children playing in the backyard, on the swingset, in the dirt and making up whatever games their fancies suggest.
I think sometimes we structure our time so strictly that we don't have time to enjoy just allowing life to "happen." Kids need spontaneity and happenstance just as much as adults do.
Maybe it's time to think less about "play dates" and more about just "playing" in general.