Name of a desolate place in Greek mythology or legend?

The Asphodel Fields, which, I'm sorry, is one the three layers of Hades, but still sounds exactly what you are looking for. Big gray plain filled with gray asphodel, gray sky, and faded spirits (spirits=ghosts/dead people). It's barren (the asphodel doesn't count as a plant), desolate ( why do you think all the spirits are faded), empty (again the asphodel and spirits don't count), and not evil/bad. It's simply where those who haven't done anything to deserve the Elysian Fields or Tartarus go (in other words, most people).

My personal opinion is that it's the worst of the three; at least in Tartarus you keep your identity. In the Asphodel Fields you just -fade.

You could try the home of the gods hypnos and thanatos, which is a pretty gloomy place. The goddess night also resides there.There really isn't a better place than Hades although I do see what you mean.

Or you could try the home of the fates, who themselves were very gloomy and desolate.

Calypso Island.

its a lovely place that I think Odysseus had past through.

The Cyclones

Aeaea--Land of Circes, the Enchantress

The island of the Sirens

The Wandering Rocks

Ogygia

Mt. Olympus (the real mountain, on top of it is Olympus, home of the gods)

Most of these places were visted by Odysseus

You could write about the labyrinth that was created by Daedalus. Very desolate.

There's also Tartarus. It is a deep, gloomy place.

hades, the under world place