「」。
She said to me, "Let's go shopping."
Literal
She [topic-は] me [to-に] 「shopping [for-に] let's go」 [quotative-と] said.
Direct quotation of an invitation. 行こう is the volitional form of 行く ('go'), used here as 'let's go' — the Japanese volitional doubles as a proposal to the listener. The 買い物に of 買い物に行く is the masu-stem + に purposive: 買い物 ('shopping, the act of buying') functions like a verb stem, with に marking the purpose of going. The same pattern shows up across casual invitations: 食べに行こう ('let's go eat'), 飲みに行こう ('let's go for a drink').