Fortunately, I know such place. Ever since the Marines and my Reserves duty that followed I was visiting the beach in Camp Sheridan.
42°13'21.7"N 87°48'27.0"W
Previously, it had the vehicle access the the beach, but now they closed it off with the big signs "Government Property" and the chain across the road, so it became nice and quiet.
Today, on it's two miles of the shore there was only on person there, locals occassionally come, but over all it is an assylum from the city crowd.
Welcome nature!
P.S. The area of Camp Sheridan was subsequently converted to suburb development, which is good, but it lost some mystique to me.