When I walk down the stairs where does my potential energy go? When I leave my room I walk down three flights of stairs releasing about 7kJ of potential energy. Where does it go? Is it all getting dispersed into heat and sound? Is that heat being generated at the point of impact between my feet and the ground, or is it within my muscles?
Related question, how much energy do I consume by walking? Obviously there's the work I'm doing against air resistance, but I feel like that doesn't account for all the energy I use when walking.
 A: The potential energy of your body starting at a height is gradually lost with each step.
Your body is transferring this potential energy into the stretching and flexing of your muscles, and the heat created by this. Some of the energy is also lost due to friction from your feet or shoes in contact with the stairs, some is lost to air resistance and sound.
Basically, a majority of the potential energy is gradually lost to biological and biochemical processes (generating heat).
A: The heat is predominantly generated in your muscles.
More direct conversion of potential energy to heat is when a person is sliding down a pole to get to a lower floor quickly. With sufficient friction, the descent is at a constant velocity instead of accelerating.
In muscle, some structures slide along each other. Muscle contraction is those structures being made to move relative to each other, using molecular motors that act somewhat like a hand-over-hand method.
As we know, muscles can also extend in a controlled manner. If you are bending down to the ground you allow your muscles to extend while maintaining tension, so that your motion is controlled.
During that controlled extending: potential energy converts to heat in the muscles.
This conversion of potential energy is on top of the baseline heat generation because the muscle is active.
When you stand up your muscles are working against gravity, actively contracting. The energy source for that contraction is, ultimately, the food you have eaten.  In the muscles, the conversion of chemical energy is not 100% efficient. A percentage is transformed to actual power output, a percentage becomes heat straightaway.
When you are allowing your muscles to extend in a controlled manner your muscles are active, so some heat is generated just because the muscle is active.
When you are walking downstairs the total heat generated in the muscles is the sum of two contributions: heat that is generated anyway because the muscle is active, and heat generated because the process of a muscle being extended against muscle tension is work being done on the muscle, and that leads to heat generation in the muscle. (That is, that heat is not  generated in the muscle when a completely relaxed muscle is extended by an external force.)

In walking we use our leg muscles actively to smooth out the motion; the leg muscles are used actively to provide some level of elastic suspension.
By comparison, kangaroos are known to have Achilles tendons that are optimized to store elastic energy. The jumping form of travelling that kangaroos can do is quite energy-efficient. The power needed for the next jump is mostly from elastic energy stored in the tendon on coming down.
Human walking doesn't have that level of efficiency. Muscle power is used actively both when the centre of mass of the body comes down and when the centre of mass of the body comes back up again. So there is the generation of heat from that power output.
A: As you take a step, you accelerate for a short while, before coming to rest again. Then you step down further. This way you cyclically reduce yourself from a higher level(energy or otherwise) to a lower one in steps, no pun intended.
At the end of each step, you come to an abrupt stop. That's because you suffer an inelastic collision with the step. The step exerts a force on you upon contact, stopping you. Since you don't bounce, the collision is inelastic.
The resulting energy loss could be to the ground (stiff stairs) or be shock absorbed and dissipated in your legs (steep stairs), go into silent deformation (soft stairs), be eaten up by friction (wide & rough stairs) or be lost as expletives (thorny stairs)!.
As mentioned in other answers, if you are the system, the earth is the surroundings. So if you lose energy, the earth gains it.

how much energy do I consume by walking?

You rightly conjectured that at a walking pace, the loss to air drag is negligible. So what is the work being done against? It's actually to again accelerate you forth. As one walks, one pushes against the ground gaining energy, then losses some on re-impact on the following step. There's definitely energy being lost, so it must be supplied. The exact kinematics or biomechanics aren't easy to model. As a rough estimate, if you are moving with speed $v$ and in each step, you generate, again grossly speaking, an average force of $F$, then your walking is dissipating energy at the rate $Fv$.

Footnote: The above discussion of energy loss via inelastic collision is, like many other answers, a simplified view. As I remarked the actual biomechanics of walking or going down steps are more refined and evolved. In particular, in the case of stepping downstairs, our body has learned to slow itself right before landing. We step gently not abruptly. To achieve this, our muscles do work by extending/contracting to exert control - that takes a lot of work too. See Cleonis's answer above for that perspective.
A: Yes, once you are standing still at the bottom of the stairs then all of the potential energy you had at the top of the stairs has been transformed into heat (due to friction and heat produced by your body) and sound waves. And even the energy in the sound waves ends up as heat once it has been absorbed by the walls, floor, ceiling etc.
A: Make it simple. If a mass of your weight fell down  the height of  three flights of stairs through the air, when it landed where would the kinetic energy accumulated by falling go?

*

*moving the earth for  conservation of momentum


*dissipated in heat on the ground


*deformation of the matter of the weight


*sound
That is why humans invented the stairs, to dissipate the kinetic energy acquired in small increments, in the same but in a  non-human-frame-destructive way.
A: There is a nice answer by @annav, I would like to add something none of the answers mention, that is atmospheric pressure.
However small the atmospheric pressure is changing when you walk down the stars, it does change, and it means that as you descend, your body must take more pressure.

At low altitudes above sea level, the pressure decreases by about 1.2 kPa (12 hPa) for every 100 metres.

https://en.wikipedia.org/wiki/Atmospheric_pressure
As the atmospheric pressure rises (when you walk down the stairs), your body needs to act against it (so your body needs to adjust accordingly), and this needs energy from the body.
A: Potential energy and kinetic energy constantly convert between each other. The conversion is not perfect as some energy is dissipated into friction and deformation of materials.
When going down stairs, your brain has learnt to let your body fall in a controlled manner. How? If you move your body horizontally beyond the edge of the step, you can decrease the force you apply in the leg still in contact with the ground and gravity will accelerate your body downwards. Your potential energy is almost entirely converted to kinetic energy during that acceleration. As your forward foot reaches the step below, it must slow down your body, ie generate a force opposite to gravity. This uses energy stored in our cells. If you stop on that next step, then you've had to dissipate the kinetic energy you've converted from potential energy. It dissipates into your body almost entirely, with very small amount in friction between floor and feet. The dissipation is in heat and friction. The friction causes heat but also atoms to get dislodged ie nanoscopic damage to your tissues, and some of the energy goes there. Your tissues heal in due course.
That's why bigger steps are uncomfortable, the energy to dissipate increases quickly with step height. And that's why going down a thousand steps in a controlled manner is actually very demanding on your body, you've caused a noticeable amount of wear on your body and heat in your muscles. If you get rest, you will convert energy from food into repairing your tissues (muscles, cartilage, ligaments etc) so they are ready for the next flight of stairs - and most likely to go up it!).
Our brains learn how to optimize the motion when we go down many steps in sequence, so we have less energy to dissipate: we don't need to completely stop our body at each step, so we apply just enough force for the net acceleration to be zero, and our motion is as near constant speed down the flight of stairs as we are able. We've learnt to change this counter force constantly as we move down from one step to the next.
Go ahead, try going down a flight of steps but completely stop your body at each step. Remember to alternate which foot goes down at each step.
A: Into the motion of your body.
When you go down the stairs, your muscles take the vertical motion down the stairs and add a horizontal component to it. As you travel down the stairs, you will be accelerated vertically by gravity, as your potential energy is converted into kinetic energy. The faster you go vertically, the faster you go horizontally, so unless you deliberately slow yourself down, you're going a lot faster horizontally at the bottom of the stairs than you were at the top of them. As a result, in addition to the conversions into heat and sound energy covered by other answers, a portion of the potential energy you possessed at the top of the stairs has been converted into kinetic energy.
A: This is easily tested experimentally. If you walked down a longer staircase, such as subway escalator, as fast as possible, you would feel that most of the energy have been be dissipated as heat in shin muscles and tendons. Then it rapidly moves with blood flow into the rest of your body.
Energy consumption for 5km/h walking is 4 calories per kilometer per kilogram of weight.
