The poem does its fair share of moving about, but most of the action occurs in otherworldly locations. It's the space of myths, and in this space we find Adonais newly-dead. The gods and personified elements of nature visit his body there, forming a procession of supernatural mourners.
Then, we move about the earth as part of a spiritual force, one that unites every living thing. In true pastoral fashion, much time is spent describing nature with vivid imagery, mentioning forest, flowers, trees, and the elements. But we don't stay earth-bound for long; next, the speaker spends some time in the kingdom of death, which isn't unpleasant. In fact, by the end of the poem, the speaker thinks conditions there are better than earth.
Rome, too, is the setting for several stanzas. The speaker describes the ruins of the Roman empire poking through the ground like "bones of Desolation's nakedness" (437), which would describe a more modern Rome than the one existing in the same era when Greek mythology was written.
The setting when the poem was written is important, too. In 1821, the Romantic poets were writing emotional, nature-filled poems full of allusion. Shelley was a major figure in this movement, as was Keats. The poem's settings are in keeping with what other Romantic poets were doing, and they reflect the beliefs of the Romantics, who wanted to fill their poetry with raw feeling and natural imagery. The poem is set as much in the landscape of other Romantic poets as it is in otherworldly locales.