Emitter-Follower Base Input Impedance
What are the general rules for figuring out the input impedances when
  looking into the base, emitter or collector?


These are general rules: -

Looking into the collector you will generally find a high impedance (assuming the transistor is operating linearly in the "active region"): -



In the active region you can see that if you increase Vce the collector current only rises a small amount. Look at the graph where base current is 0.3 mA; when Vce is 5V, Ic is about 10 mA and, if you increased Vce to 20 volts maybe Ic has increased to 10.5 mA. So, there is a dynamic impedance of 15 volts divided by 0.5 mA and, this is a dynamic resistance of 30 kohm.

If you look into the emitter you will find a harder place impedance wise and, as a general simple rule, the impedance is just a few tens of ohms - think about an emitter follower - it has a low output impedance (the same as the input impedance looking in) because if the load impedance reduced, then the base-emitter would turn on a tad more and the collector current would compensate this by keeping the voltage at the emitter nearly the same.

When looking into the base you have to consider the emitter resistor and, in an emitter follower circuit, this emitter resistor is sometimes loaded with another resistor such as in the picture in the question. 

So, the emitter resistor becomes Re||Rload or \$\dfrac{R_e.R_{load}}{R_e + R_{load}}\$ and this should start to look familiar as being part of the equation in your question. Because of current gain this combined emitter resistance is transferred to the base by multiplying by hFE. Ultimately the impedance you calculate will be in parallel with the base bias resistors so there is another step to calculate input impedance rather than just the impedance looking into the base.