The concept

Walking is kind of unique, in that it offers a variety of opportunities to exercise your awareness and perception.

Movement

Conveyor belt - Shift your perception to the sense that you are standing still, and the world is moving. Perhaps the world is a treadmill, and you are merely "keeping up" with its motion. Or perhaps you are standing still and the world is morphing or warping in a way that brings things closer to you or farther from you.
Timeless walking - Notice a fixed marker such as a light pole, and as you walk towards it, shift your perception to the sense that you are in fact not walking at all, because without any "time" beyond the now, you will simply always be as close to that marker as you are, and there is no change in that distance, because each moment exists independently, and each "new now" simply exists with its own facts about reality.
- Stairs - do the same exercise when on stairs, as it is even easier. Whenever you take a step, pause for just a split second with one foot on the new step and one foot on the previous step. Notice that you have arrived at this location, and this is the present moment. After each step note that you are in the present moment. There is no journey, just present moments. Once you've learned to see this, learn to see it without any mental or actual pauses in your steps.

Walking is an opportunity to observe and experience Connected Systems.

Walking is a perfect time to perform Headless Exercises. Try the following types of things.

Become headless (if you don't know about this, follow the links)
Become aware of your surroundings in an open, spacious way, noticing how that space includes the location where your head should be
Expand your headless awareness to your whole body, letting go of the sense of self, ultimately feeling the flow of your walking as a property of Now, rather than something You are doing or experiencing.