The story begins in the uncharted backwaters of the unfashionable end of the western spiral arm of the galaxy.
More specifically, the story begins on Earth, "an utterly insignificant blue-green planet".
Even more specifically, the story begins in the West Country, the quiet, rural part of south-western England where Arthur Dent lives. Later in the series it is mentioned that Arthur Dent bought his towel in Salisbury, so it is fair to assume he lived near there.
A legendary lost planet that used to be the centre of the bespoke planet building industry. After a universal economic crash meant even the ludicrously wealthy could no longer afford their wares, the inhabitants shut up shop to wait for economic recovery.
The surface of the planet is an utterly desolate wasteland. In the TV adaptation these scenes were shot in a claypit in Cornwall. See pictures here. Douglas Adams was always very disappointed by this and had initially wanted to film these scenes in Iceland.