There are lots of options for playgroups, my church hosts one twice a month, and there are a variety offered through each base (usually through the community center or if you're army through ACS including a group for ESL to practice their English) and we're a part of a playgroup called Kinyoubi Kids, we meet every friday at different locations:
http://groups.yahoo.com/group/KinyobiKids/
April 4th - Dolphin Park
April 11th - Araha Beach/Pirate ship park
April 14th - Okinawa City Athletic Field
April 25th - Manta Park
As usual, we meet at 10am and please bring something to share for our potluck lunch. In case of rain, an alternate location will be announced by 8:30am that morning.