"Going the wagon" is a colloquial phrase that is often used to refer to travelling, moving or making a journey. There are many synonyms that can be used to replace this phrase and convey the same meaning. Some of the common ones include "hitting the road", "setting off", "embarking on a journey", "taking a trip", "starting out", "commencing travel", "going on a voyage", "heading out", "journeying", and "travelling". All of these synonyms can be used interchangeably and add variety to writing or speaking, making it interesting and colorful. So, the next time you need to say "going the wagon", try using one of these synonyms instead.