There are many synonyms for the phrase "travel on foot." Some of the most common ones include walking, hiking, trekking, strolling, and perambulating. Other words that can be used to describe the act of traveling on foot include rambling, meandering, roving, sauntering, and wandering. Each of these words conveys a slightly different nuance or connotation, and the best choice will often depend on the particular context or situation. For example, hiking might be more appropriate when referring to a trek through the wilderness, while strolling is often used to describe a more leisurely pace through an urban area.