Ouch. I'm in Indiana. Half the parks in the city have grills. The only time you need to pay a fee in the city is if you rent a pavilion.
I'll assume those permit fees are to keep the homeless population at bay or you live in a fire hazard area.
Bummer. I think the only thing left for you is have it at home or pay the permit fee. Any way you slice it, though, you definitely want to bring it up the next time your city council meets. Find out the actual "why" of the fee. Go in to argue your point. Back it up with facts.
I know California has a higher cost of living, but still, $60 is a bit much. Looks like you'll either have to serve cold food, or cook it off site.
Remember, crank case cooking is also an option.