I am trying find a phrase or just a word that expresses the friend who travels with you along your trip or journey.
You are my best ____ .
How can I call this person?
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You could use any of the following:
travelling companion / travelmate / travel partner
Myself, I would probably favour "travelling companion".
Edit: As several people have pointed out, the word "companion" alone would be sufficient.
Buddy is, a friend or partner for a particular activity, and it is often used in that sense. E.g, "climbing buddy", "diving buddy", etc.
You are my best companion is technically correct, but not something someone would ever say, because 'best' implies a comparison that is not appropriate to the term 'companion', given the modern broadening of the meaning of the word. Buddy still has a limited range of interpretation though, and so
You are my best travelling buddy is something that one might actually hear.
You can call the person your peripatetic. https://www.google.com/search?q=name+someone+that+accompanies+you+on+trips+-+how+to+answer&oq=n&aqs=chrome.0.69i59j69i57j69i59j0l5.12986j0j8&sourceid=chrome&ie=UTF-8