Assuming you'll want to read Fall of Hyperion, the continuation of Hyperion (can't really call it a sequel), it's interesting that Keats plays an even larger role in that book. Simmons includes all sorts of parallels between his work and that of Keats, but I even found myself a bit annoyed at times as it seemed like Simmons wrote the second part of the book mainly to show his love for Keats.
Still, Hyperion and Fall of Hyperion is some of the best scifi I've read, and I say this despite not being a big fan of some of the themes Fall introduces.
Since you're reading Hyperion, you might be interested to know the reference to Hyperion and Fall of Hyperion (Poems by Keats, not the Simmons books which share the same names).
You say you're almost done, so I assume you have read the soldier's tale by now:
> The Fall of Hyperion is narrated by the poet, who, in a dream, is allowed to enter a shrine. The goddess Moneta reveals to the dreamer that the function of the poet in the world is to separate himself from the mere dreamer and to enter into and embrace the suffering of humanity.