It's not called our "walk" for nothing.
"The steps of a good man (and woman) are ordered by the Lord, and He delighteth in [their] way." (Psalm 37:23)
Perambulate
To walk about. In referring to Australian Aborigines, the Walkabout is more akin to a Vision Quest. A leave of absence from the rest of society in order to find oneself, to get something that was theretofore unavailable to the seeker in the closed-off and disjoint place from which they came. I find walking essential. A quick stroll around the block. Opting to walk, instead of drive, to the store. Really, any instance where one foot must be put in front of the other--numerous times, I might add--in order to reach a destination. I feel more in touch with a baser level of existence when I walk. But where am I going? It's not enough to just hoof it. I'm serious. Walking clears my head. It gets me out of the prescribed way of thinking that says I must always be doing something at the pace of everyone else. That's a hard one to outstride, I might add. Life is best lived in relation to God and His pace.
"what doth the Lord require of thee, but to...walk humbly with thy God?" (Micah 6:8)
Peregrinate
It means the same. A deeper shade of "searching" begins to show, however. Now, you're not just wandering around, you've caught the scent of something. But what? The Hebrew word derek means "road". It's translated in the Psalms as "way" and "ways". It's referring to God's word: "Teach me, O Lord, the way of the statutes; and I shall keep it unto the end." A road comes and goes. We didn't pave it and upon setting foot on it, don't know where it leads. While it's one thing to "blaze a trail", as Christians, we can't go anywhere that Jesus hasn't paved the way for us, first. This is why He says "whosoever will come after me, let him deny himself, and take up his cross, and follow me." (Mark 8:34) When He says "take up (my) cross", it means to surrender this notion that I can find what I'm looking for on my own. That, out of all the paths available to me, even the ones that I'd like to wear in for myself, Jesus knows where I'm headed and where I should be going. And don't immediately think that the two are already mutually exclusive.
"For the ways of man are before the eyes of the Lord, and He pondereth all his goings." (Proverbs 5:21)
Peripatetic
Aristotle taught as he walked. His 'Peripatetic school' was so-named for that reason. While the word does refer to his school--and his way of doing things, it also simply means to just "walk about". Jesus taught as He walked as well. And as He was always following the Father, we'd do well to follow Him. A one-track mind has both positive and negative connotations. I suppose it all depends on where that one track is headed. Stay the course. If you find yourself on a path that you begin to glimpse is leading nowhere, take heart. Jesus walked every path, even the one you're on now. And abandoning every metaphor and simile and aphorism, I will say that He has the ability to turn the track on which you are (metaphor! It's kinda hard...), to where He knows you're supposed to be headed. Trust Him. He's already walking alongside you by His Spirit.
"All the paths of the Lord are mercy and truth unto such as keep His covenant and His testimonies." (Psalm 25:10)