There are a couple of nice shelter houses in Pickerington that you can rent (they are very reasonable!). I have rented these shelters for my daughter's and son's parties many times.....as well as family get togethers. There is a children's play area right by both of the shelters and there is tennis, basketball, plus plenty of room to set up volleyball if you like. The phone number to reserve the shelters is ###-###-####. You can find out more about the shelters at www.pickerington.net.
One other idea is Slate Run....for my daughter's 2nd birhthday, we went to Slate Run park for cookies and apple cider and playtime....then we all hopped in our cars and followed each other to Slate Run Historical Farm.....the kids had a ball there also! You might want to call Slate Run and see if you can rent shelters or if they will organize anything for birthday parties. Here are their websites.... http://www.metroparks.net/ParksSlateRun.aspx and http://www.metroparks.net/ParksSlateRunFarm.aspx. A couple of phone numbers are ###-###-#### and ###-###-####.
A few last suggestions.....Three Creeks Metro Park and Chesnut Ridge Park or even Old Man's Cave. Websites: http://www.metroparks.net/ParksThreeCreeks.aspx and http://www.metroparks.net/ParksChestnutRidge.aspx and http://www.dnr.state.oh.us/parks/tabid/743/Default.aspx.
Good luck with the party!
T.