Where It All Goes Down
Denmark, around Year...800? 900? 1000?
Because Gardner is playing around with the source material from Beowulf, we can say with confidence that Grendel frolics through the forests of Denmark. But the date? If the novel inherits the problem of setting from the poem, we have no way of knowing whether the events are from a glorious past (like 500 or 600 CE) or from the much later date of the poem's actual composition (1000 CE).
Gardner doesn't do much to clarify the time frame for us—though we know from the conversation with the dragon that it's at a time before some of the more subtle scientific discoveries (like atoms). Nor does it seem to matter much. Gardner freely adapts all kinds of sources material, from medieval epic to modern philosophy—to create a unique, dreamlike location outside of normal time.