General:
* Nomad
* Roamer
* Stroller
* Drifter
* Wayfarer
* Vagabond
* Itinerant
* Pilgrim
More specific:
* Sojourner (someone who stays in a place for a short time)
* Exile (someone forced to leave their home)
* Fugitive (someone running away from the law)
* Explorer (someone who travels to new places)
* Adventurer (someone who seeks out exciting experiences)
Figurative:
* Errant (wandering from the right path)
* Astray (lost or confused)
* Unmoored (without a sense of direction)
The best synonym will depend on the specific context and what you want to emphasize about the wanderer.