Will give the park a call later.
Edit: Gave them a call if we have 5 or more people (I hope we have) we have to book some sort of reservation (don't think it should cost anything). Entry fee is $6 per car and the picnic sites are right off the parking lot.
McDowell Mountain Regional Park offers two picnic areas totaling 88 picnic sites. Each site has a picnic table, restroom, playground, and barbecue grill. Picnic sites are available on a first-come, first-served basis.
Ironwood - open year round.
Paloverde - closed from May until August.
Is this too far?
Will see if the North/Phoenix Mountain Preserves have picnic areas. I heard south mountain can be pretty sketchy so I'm not going to try that.