There are several synonyms for the phrase "walk about" that can be used to add variety and depth to your writing. One option is "amble," which suggests a leisurely and easygoing walk. A "saunter" is similar but has a more carefree connotation. "Stroll" is another option that implies a relaxed and meandering walk. For a more purposeful walk, "stride" or "march" may be used. "Perambulate" is a formal synonym that can be used to describe a slow, deliberate walk. Finally, "wander" is a versatile synonym that can convey an aimless or exploratory walk, depending on the context.