Riverside County and San Bernardino County to the north form this metro area. Like many such metro areas in the Southwest, it extends far into uninhabited desert areas, in this case east through the Mojave Desert to the Nevada/Arizona border. Larger than nine U.S. states, it is often referred to as the Inland Empire.
I agree with tchrist that the word doctor in doctor appointment is a noun (attributive noun I believe), although the definition of an attributive noun is a noun used as an adjective, so maybe it's just semantics at some point.
As the doctor also has an appointment with you, doctor's appointment is unequivocally correct in its own right. It is also by far the most common as a set phrase: Any other plural usage would be entirely subjective, but I don't feel doctors appointment would be appropriate under any circumstance.