Drift: This implies a gentle, almost unconscious movement, like being carried by the wind.
Wander: A more common term, suggesting exploration and lack of direction.
Meander: This describes a winding, curving path, often along a river or stream.
Stroll: A leisurely and relaxed walk, with no particular destination in mind.
Saunter: A slow, unhurried walk, often with a confident or nonchalant air.
Roam: This implies a wider range of movement, suggesting a search for something unknown.
Amble: A leisurely, unhurried walk, often with a gentle swaying motion.
Promenade: A formal and elegant walk, often taken for pleasure or display.
Ramble: A long, aimless walk, often with no clear route in mind.
Stray: This implies losing one's way or deviating from a planned route.
Err: This suggests making mistakes or taking the wrong path.
The best verb to use will depend on the specific context and the feeling you want to convey.