Where It All Goes Down
From Bede's detailed backstory, we happen to know exactly where Caedmon was when he first recited this hymn: in a barn with an audience of one extremely powerful angel begging for a song. "I don't know how to sing," Caedmon protested (according to Bede). But the angel wasn't chilling in a cow barn for nothing. He was there for some late-night entertainment and snapped back with, "Nevertheless, you must sing."
But let's step back from the legendary context for a moment and consider the implied setting of the poem itself. Obviously this is a religious poem since its subject is God's creation of the universe, and that means the "we" of the first line is speaking on behalf of a larger Christian community.
What settings would be appropriate for this kind of poem? Monasteries and convents, churches—really anywhere that a lot of pious medieval people might gather. Wherever this poem takes place, it's clear that the main focus is on a higher setting than the one here on Earth: heaven.