General:
* Stroll: A leisurely walk
* Amble: A slow, relaxed walk
* Saunter: A leisurely walk with a slight swagger
* Wander: To walk without a fixed destination
* Roam: To wander freely over a wide area
* Prance: To walk with a lively, spirited gait
* Stride: A long step in walking
* March: To walk in a steady, purposeful way
* Pace: To walk at a steady, measured speed
* Traverse: To cross or travel across
More specific:
* Trot: To walk briskly
* Shuffle: To walk with short, slow steps
* Skip: To walk with a light, bounding step
* Scamper: To run quickly and lightly, usually with short steps
* Tiptoe: To walk on the tips of one's toes
* Limp: To walk with a noticeable difficulty
* Hike: To walk for a long distance, especially in the countryside
* Trek: To make a long, arduous journey on foot
The best synonym to use will depend on the specific situation.