【Wander】 , 【stray】 ,  【roam】 ,  【ramble】 ,  【rove】 ,  【range】 ,  【prowl】 ,  【gad】 ,  【gallivant】 ,  【traipse】 ,  【meander】  can mean to move about more or less aimlessly or without a plan from place to place or from point to point.

Most of these verbs may imply walking, but most are not restricted in their reference to human beings or to any particular means of locomotion.

【Wander】 implies the absence of a fixed course or more or less indifference to a course that has been fixed or otherwise indicated; the term may imply the movement of a walker whether human or animal or of any traveler, but it may be used of anything capable of direction or control that is permitted to move aimlessly.

【Stray】 carries a stronger suggestion of deviation from a fixed, true, or proper course, and often connotes a being lost or a danger of being lost.

【Roam】  carries a stronger suggestion of freedom and of scope than  【wander】 ; it usually carries no implication of a definite object or goal, but it seldom suggests futility or fruitlessness and often connotes delight or enjoyment.

【Ramble】 , in contrast, suggests carelessness in wandering and more or less indifference to one’s path or goal. It often, especially in its extended uses, implies a straying beyond bounds, an inattention to details that ought to serve as guides, or an inability to proceed directly or under proper restrictions.

【Rove】  comes close to  【roam】 in its implication of wandering over extensive territory, but it usually carries a suggestion of zest in the activity, and does not preclude the possibility of a definite end or purpose.

【Range】  is often used in place of  【rove】 without loss; it may be preferred when literal wandering is not implied or when the stress is on the sweep of territory covered rather than on the form of locomotion involved.

【Prowl】 implies a stealthy or furtive roving, especially in search of prey or booty. It is used not only of animals, but often also of human beings intent on marauding, but it is also applied with little or no connotation of an evil intention to persons, especially those of a restless or vagabond temperament, who 【rove】 , often singly, through the streets or the fields in a quiet and leisurely manner.

【Gad】  and  【gallivant】  imply a wandering or roving especially by those who ought to be under restrictions (as servants, children, husbands or wives, and persons who have not much strength or enough money).

【Gad】  , usually with about , may suggest a bustling from place to place idly or for the most trivial ends and often to the detriment of one’s actual duties.

【Gallivant】  adds to  【gad】 the implication of a search for pleasure or amusement or the use of an opportunity to display one’s finery.

【Traipse】  , which commonly suggests more vigor in movement and less aimlessness in intent than the remaining terms, may come close to come , go , or travel in meaning.

Even when used with reference to an erratic course  【traipse】 ordinarily implies a positive purpose or stresses a bustling activity or a wearying expenditure of energy.

Sometimes the term loses most of its reference to a course and then stresses a dashing or flaunting manner of going.

【Meander】 may be used in reference to persons and animals but more characteristically in reference to things (as streams, paths, or roads) that follow a winding or intricate course in such a way as to suggest aimless or listless wandering.