Formal:
* Stroll: This is a common and generally neutral synonym.
* Walk: This is another common and neutral synonym.
* Amble: This suggests a leisurely pace.
* Saunter: This suggests a relaxed and unhurried walk.
* Promenade: This suggests a formal or leisurely walk, often in a public place.
* Traverse: This emphasizes covering a distance, often in a specific direction.
Informal:
* Wander: This suggests aimless movement.
* Roam: This suggests exploring a large area.
* Meander: This suggests a winding path.
* Pottle about: This is a British colloquialism for strolling aimlessly.
The best synonym will depend on the specific context and the tone you want to convey.