I want my mug to boil as soon as possible and I prefer not to throw energy away. Where in microwave ovens things warm faster?
Microwave ovens are designed to spread their energy around inside the oven chamber in the most uniform way possible, so that any food placed in them will get uniformly heated and cooked. This means it shouldn't matter where in the oven you place your mug when heating it.
Depending on the design of the oven, uniformity can be aided by something called a mode mixer which bends the microwave beam around in a variety of directions as it enters the oven chamber, and by the use of a turntable which rotates the food item around under the beam so it gets uniformly "illuminated".
You can map the uniformity of the microwaves in the oven if you want by covering the bottom surface of the oven with marshmallows and then turning it on until you first notice the marshmallows beginning to melt. The first ones to melt are sitting in a "hot spot" where the microwaves are concentrated.
Don't let this process carry on too long, for the melted marshmallows are messy to clean up!
Consider the microwaves as a light. It is absorbed first at the surfaces. The plate rotates to make the light heat the water more uniformly. The oven walls reflect the light, so it is not lost.