I would call it a "Journey" Dog

Dirk Gently's Guiding Eyes for the Blind

While backpacking in Ireland, my friend and I visited the small island of Inish Oirr. We had all day to explore the island so set off without any route planned. A black dog tagged along and soon started guiding our way. He would loop back and stop to wait for us at turns. We followed him blindly through the maze of stone walls. He led us to a lake, a lighthouse, and a shipwreck. He always seemed excited to show us the next landmark. We literally followed a dog from morning until sunset. It felt as though he had done this many times before. He was such a good boy.

The park. You're going to the park. Everyday. If you live in a warm environment with a beach, that's where you're going. That park.

Not all those who wander are lost. Sometimes they just play dog roulette

As long as you don't mind going to all the smelliest places.

I have a Shiba. Walking her is like walking a cat, so I beg to differ

sometimes I just close my eyes and see where my dog takes me, is fun, mentally hard, but fun.

That's why I call my cat a guide cat. He guides me to lolll around on the couch for 22h a day

Similarly helpful advice: a broken clock still shows the correct time twice a day.

Man you are just ripping off my welcome mat.

You may not end up where you meant to go, but you’ll end up somewhere interesting

This is a great quote. Describes how I feel at my job at the moment ...

Can I use it?

Might get kind of tricky when crossing a busy street

I'd say a dog would still go to predictable places eg. they'd go for a walk on their usual route (maybe a bit larger).