Visible crew/equipment: When the astronauts are running down a dusty hill in the desert, you can spot the shadow of the camera on the back of Landon and Dodge. (00:15:50)
Visible crew/equipment: Right before Taylor gives the female ape (Zira) the piece of paper with his name on it, while he is fighting the other ape, the shadow of the camera is seen on the bottom of the cage. (00:47:05)
Visible crew/equipment: After Taylor flees the market, he enters a museum and begins to run down a spiral staircase. As he reaches the bottom of the staircase, to the right of shot, a cameraman's shadow is visible on one of the carvings and the staircase's support column. (00:55:30)
Visible crew/equipment: After Taylor exits the museum he is whipped by an ape on a horse. Taylor/Charlton Heston is replaced by a noticeable stunt. (00:58:57)
Visible crew/equipment: When Zira locks Nova in Taylor's cell watch the left iron bar and you'll see the shadow of the camera approaching.
Answer: He's in the same location as Ellis Island. Thousands of years have resulted in significant changes geographically.