traipse
To walk around tiredly, often wandering without much purpose.
To traipse means to walk somewhere in a tired or reluctant way, often over a long distance or through difficult conditions. When you traipse through mud after a rainstorm, your feet drag a little and each step feels like more effort than it should. When you traipse all over the mall looking for a specific pair of shoes, you're wandering from store to store with growing weariness.
The word captures both the physical movement and the feeling behind it. You don't traipse when you're excited and energetic: you traipse when you're worn out, when your legs feel heavy, or when you'd rather be somewhere else. A kid might traipse home after a long day at school, tired and ready to rest. A family might traipse through an enormous museum, feet aching after hours of looking at exhibits.
Traipse can suggest aimless or inefficient movement too. If someone asks where you've been and you say, “Oh, I've been traipsing around town all afternoon,” you're implying you wandered without much purpose, probably getting more tired than you planned.