Lyon Village and Lyon Park Community Houses in North Arlington have special children's birthday party facility rental rates, even for the general public. Last I checked it was Sat am $100 for 4-hours. There are also other rate options, days. The LV one is next to a nice children's park. The LP one has outdoor grounds included.
LV CH address: 414 N Fillmore St Arlington, phone 703-527-9520.
If I recall correctly, alcohol is fine but no kegs. There is a security deposit.