Just as when you eat your soup: an outer edge at the top will result in the coolest area. This is because the edge of the container contacts the air, transferring heat, in addition to heat being transferred from the top. Additionally, the area from which heat flows from the rest of the coffee into the outer edge area is relatively small when compared to any other location.

First of all one could argue that drinking hot coffee is a bad idea, you could burn you tongue/throat as your lips have no indication of how hot the liquid is.

Second, assuming I understand the question right I would rephrase it to “What is the best place to position a stray when drinking hot coffee in order to get the least hot coffee?”

The above solution seems to be the best one, at the top outer edge the heat from the coffee can be transfered by means of conduction (liquid in contact with the container), infrared radiation into space and, most importantly, evaporation. And the hotter the liquid the faster this process goes. If indeed the outer edges are quickly cooled down, one could even speed up the process of overall cooling down by using the straw to stir the coffee, getting the hotter lower layers to mix with the colder layers increasing the temperature at the top outer edges causing it to cool more rapidly. Of this happens automatically through convection (hot liquid rises, cool liquid falls to the bottom) but stirring it would definitely speed up that process.

Drinking coffee with straw is a sin!

But if there is no ice cube I would go for either the upper edge or the lower corner of the cup.
I think that it may depend on the cup. Is it a Styrofoam cup or a mug? A mug will have more thermo mass. The area with the most thermo mass to coffee ratio should be in the lower corner under the handle connection. The handle warms up so it is diffusing heat from the coffee into the surrounding environment ie. hand and air. The bottom of the mug will be sitting on a surface maybe an aluminum or steel desk and that will conduct heat away from the mug also. All of this cooled coffee will remain at the bottom to be sucked up the straw, but then when it is being sucked up it will pass through the warmer upper coffee and then warm up. so the best thing to do is to drill a hole in th bottom of the mug and place the straw in it leaving as much of the straw exposed to the environment as possible.

I know this isn’t a helpful response. Why not do the experiment? It would be sooo easy! Who drinks coffee with a straw anyway? If you’re worried about yellow teeth, DRINK MILK!

Heat does not rise… hot air rises.

Heat is energy in transit, and what we measure as temperature is actually the amount of energy contained within the substance we are measuring. So samples of higher energy (heat) within the coffee will be expected to do three things:
1) contain particles moving at higher velocity
2) give rise to convection currents
3) undergo a phase shift (turn to steam)

These three things are crucial. Because energy flows from areas of high energy to low, we can say that the natural direction for energy flow will be in the direction of the substance with the least internal energy i.e. the outside air (whether ceramic or styrofoam the material of the container matters little because in comparison to the temperature difference between the coffee and the air, the air will have a lower temperature than the walls of the cup so heat will be lost more readily to the air than to the walls of the cup)

you could argue that the fluid would be self insulation, but this sketchy at best because of thermal convection within the cup, and the inevitable motion generated by holding a cup of coffee.

The steam rising from the surface of a cup of coffee represents the particles with the highest energy actually leaving the cup (energy must be put into the coffee to complete the phase change to steam) so the steam rising from the surface of the cup is actually analogous to particle leaving the cup and taking more than their fair share of the total energy of the coffee with them. But to get out of the cup these higher energy particles must first come to the surface, (also where their is a greater temperature differential so heat will naturally flow to this surface any way).

So the area of higher energy (though not necessarily highest temperature) will tend to be at the surface of the cup when the coffee is first poured. As it cools the area of highest energy will simply become which ever area is furthest from any surface of cooler temperature than itself (i.e. the middle of the column of coffee)

In the end it makes little difference where you stick your straw because the the temperature differences will be so minute that they will be made up for as the coffee in the straw is drawn through areas of higher temperature than itself, thus reheating it. in the end you will still burn your tongue.

Perhaps consider convection currents – who among us has not seen swirling currents in coffee?

I do know for experience that drinking cold milk with a straw from the bottom of a glass makes some difference. I guess convection currents provoke the coolest milk to go to bottom (provided no stirring).
I guess we could expect similar behavior from hot coffe in a cup as for cold milk in a glass, so I definitely vote for the bottom of the cup for the place where the coolest coffe is.