Looking for buddy for 4yo son

I'm home with the kids on Tuesdays and Thursdays and since my oldest turned 4, I've noticed that the playgrounds on these days are mostly filled with younger kids. (I'm guessing lots of 4-5 year olds are in Pre-K full time!)

That said, I really would love for him to have a playmate who is close in age, if not older. Any suggestions for classes or playgrounds or places where we might find a fellow 4 year old for our Tues/Thursday adventures?