Albert Barnes Commentary Psalms 107:4

"They wandered in the wilderness in a desert way; They found no city of habitation." — Psalms 107:4 (ASV)

They wandered in the wilderness - On their return from Babylon; or, when God was conducting them again to their own land. The word “wilderness” in the Scriptures means a desolate, barren, uninhabited region, usually destitute of trees, of springs, and of water-courses. It does not denote, as it does with us, a region of extensive “forests.” Compare the notes at Matthew 4:1.

In a solitary way - Rather, in a “waste” way; a land that was desolate and uncultivated.

They found no city to dwell in - In their journeyings. This was true of the region between Babylon and Palestine; a wide, barren, desolate waste.