Are there any symbols in "On First Looking into Chapman's Homer"?

Yes, Keats uses symbolism in this sonnet. I'll identify one of them for you.

A symbol is a term used to represent something else by association. In lines 1-2, the narrator says "Much have I travell'd in the realms of gold,/ And many goodly states and kingdoms seen." We can assume that the speaker of this poem is Keats himself. When he says he has traveled to many states and kingdoms, he doesn't mean that he has literally been to other countries. He is using them to symbolize the act of reading or using the imagination. When you read, you travel to the world of the novel or the poem or the story.

Now, what symbols can you find?

MUCH have I travell'd in the realms of gold,   And many goodly states and kingdoms seen;   Round many western islands have I been Which bards in fealty to Apollo hold. Oft of one wide expanse had I been told         5  That deep-brow'd Homer ruled as his demesne:   Yet did I never breathe its pure serene Till I heard Chapman speak out loud and bold: Then felt I like some watcher of the skies   When a new planet swims into his ken;  10Or like stout Cortez, when with eagle eyes   He stared at the Pacific—and all his men Look'd at each other with a wild surmise—   Silent, upon a peak in Darien.