Is there a special parking area if you are only going to Soak City? Also is there a picnic area near Soak City where you can leave your cooler and picnic basket (similar to the area outside the main gate).
Yes, there is a Soak City lot. Tell the parking attendant and they will tell you where to go from there. As for the coolers I don't remember seeing any tables anywhere.
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There is a picnic pavilion for Soak City, it's by the west entrance.