Visit the Mysterious Giant Rock
This is quite literally a giant rock in the desert. According to most sources it's the largest freestanding boulder in the world at about 7 stories high.
Visit the Ghost Town of Amboy
The ghost town of Amboy was once a major stop along Route 66 until Interstate 40 was opened. The city only has 10 remaining buildings, Roy's gas station and motel cafe being the biggest landmarks. You can stop in for a Root Beer and wander through some of the abandoned hotel rooms with art installations.