"wandering down" is correct and usable in written English.
You can use it to describe someone or something travelling in a downward direction. Example: I watched the butterfly wandering down the garden path.
As I was wandering down the street.
It's easy to imagine them wandering down the streets.
I felt weirdly deflated wandering down to the main room.
Wandering down to the sea takes a couple of minutes.
"We wanted David to feel comfortable wandering down the hill".
Such responsiveness keeps students on track, preventing them from wandering down "garden paths" of unproductive reasoning.
Instead they have muddled along, wandering down many a dead end in the process.
It's one for fans but well worth the brief diversion before wandering down to the docks.
But Mr. Gonzalez had already left the cab and was wandering down Eighth Street.
We were wandering down the main street, reading menus, when the lights went out.
It's not uncommon to see elk wandering down near the beach or bald eagles swooping overhead.
