My family had a Sunday morning routine when I was young. We attended church in Santa Monica then drove down Ocean Avenue to the Santa Monica Pier. Back then you could drive your car down to the end of the pier and turn around. Then it was lunch at places like Callahan's, Pickle Bill's, NuWay Chili Dogs or The Apple Pan. I loved the Apple Pan. It is located on Pico right across the street from the Westside Pavillion Shopping Center. Back in the 1950s there was a child's amusement park across the street that had a little roller coaster and Ferris wheel.
The Apple Pan hasn't changed much since it opened in the late 1940s. They have the best Hickory Burgers in town. It is best to arrive when they open so you can get a seat at the horseshoe shaped counter right away.