If you will refer to the sonnet you will see that the extended metaphor begins with the very first line. Keats is not talking about his travels or about foreign states and kingdoms. He is using an extended metaphor to describe his experiences with reading. Traveling in the realms of gold is experiencing all sorts of things in his imagination by losing himself in good books. The metaphor continues all the way to the line in which he says, "Yet did I never breathe its pure serene / Till I heard Chapman speak out loud and bold."
That is the end of the metaphor. The rest of the sonnet is an extended simile, because Keats uses the word "like" and goes on to compare his feelings upon first looking into Chapman's translation of Homer to those of an astronomer discovering a new planet or like Cortez when he first saw the Pacific Ocean. So the entire sonnet is one long metaphor followed by one long simile.