The main use of symbolism is how Snodgrass uses metaphors to describe the person he wants to come live with him. He compares her to a "resort", a "braintrust", a "best beast", a "distraction", and a "location". He compares her to all of these things; if you consider each one, they all say something unique and profound about what she means to him. She is a resort-she provides a wonderful, relaxing escape for him; she is a vacation destination he greatly looks forward to visiting. She is a braintrust-she stimulates his brain and makes him ponder deeply many things in life he wouldn't have otherwise. And, so on and so forth. So, he uses metaphors to reveal deeper feelings he has about her.
Snodgrass also uses metaphors to describe his past life. He compares his past life, actions, and acquaintances to "a list", "repayments", a "cost", and a "breach". Comparing his past to these things makes his past seem burdensome and taxing; he wants her to come and cancel the cost, close the breach, and check off items on his list. He feels that her presence would wipe the slate of his past clean. So once again, metaphors-in describing his past life-help us to understand how he feels for her.
There are other forms of symbolism in there; he uses similes ("prove the day like Proust) and allusions (referring to Freud and Proust). But the main use of symbolism is through metaphors, which help us to understand the role that she plays, or that he wants her to play, in his life. I hope that helped; good luck!