In some circles, attention is focused on a few skills (shooting, primarily, but emergency/trauma medicine also) which are indeed crucial - at times - but are also among the sexier of the skills which might come in handy in some sort of crisis. In fact, if you have some of the below skills, you might not have to use the ones named above.
Side note - I have used "post-apocalyptic" in the title because it will attract attention. These things also come in handy in today's world.
If you ever leave the pavement - and sometimes even if you don't - you're going to leave tracks that can be followed. Being followed might be a problem. You might also need to follow tracks for a variety of reasons - finding a lost family member, for example, or tracking a wounded animal. I have only the most rudimentary of tracking skills. I can tell a deer print from a human, most of the time.
While tracking skills can certainly be developed, the tracking abilities of some people, in my opinion, border on the supernatural. A friend of mine is a member of BORSTAR (Border Patrol Search, Trauma, and Rescue) agent, and we recently discussed tracking. I learned a lot, but he's had years of practice, and there's really no substitute for that.
In addition to the ability to follow someone, an astonishing amount of intelligence can be gathered from prints - not only basic things like the number of people in a group, but how tired they are, how much weight they're carrying, if they're a pregnant woman, etc. If you have the chance to learn about tracking, I would not pass it up.
Sanitary Food Preparation
Puking post-partaking in poorly prepared pho is pathetic.
But a bad case of salmonella when you don't have access to medical care? Potentially fatal. And everyone who's played Oregon Trail knows how deadly dysentery is.
I first learned about sanitary procedures for food preparation and medical care from my mother, an ER nurse and gourmet chef, and later learned more from the military. If you didn't have these advantages, don't fret. Learning how to prepare food and water is fairly straightforward. The CDC has information on this exact topic.
When I was getting ready to deploy with 5th Marines, I was told how critical it was that I do a "5 and 25" whenever our vehicles stopped. Unfortunately, no one ever told me what a "5 and 25" actually was. I eventually Googled it and found that I was supposed to look for danger within 5 meters of the vehicle immediately, and within 25 meters if we stopped for a longer period of time. This was my first exposure to situational awareness in terms of armed combat.
Although scanning for IEDs isn't the same exact thing as scanning for speed traps, situational awareness is something that can be applied across a variety of tasks. It is not as simple as constantly scanning for threats, but more of a nuanced and intuitive, and sometimes passive, observation of one's surrounding area and in part looking for things that don't belong.
It can also be important to know the placement of objects when stationary - for example the layout of a room and the location of the exits before it is plunged into darkness. But it's equally important when moving, such as knowing the location of vehicles around your own as you travel down the highway, which gives you the ability to make an emergency lane change with the least possible delay when necessary.
As your speed increases, your ability to be aware of your surroundings generally decreases. If you are running across rocky ground while tracking criminal elements, you may need to focus on where to place your feet so as to avoid falls or injury. You may also need to focus on checking the bushes and trees ahead for signs of an ambush - but you may not be able to do both of these things at once while running.
Knowledge and experience both play a role when it comes to situational awareness, as does mindset. From an academic standpoint, Gavin de Becker's book "The Gift of Fear" is an excellent primer. But experience must be gained in the real world.