A short walk for pleasure or exercise

One word substitute is Stroll.

Jog: run at a steady gentle pace, especially on a regular basis as a form of physical exercise.
Stroll: walk in a leisurely way.
Gallop: the fastest pace of a horse or other quadruped, with all the feet off the ground together in each stride.
Promenade: a paved public walk, typically one along the seafront at a resort.