。
She's a sucker for chocolate cake.
Literal
She [topic-は] chocolate-cake [for-に] [no eye-目がない].
目がない is a vivid body-part idiom meaning 'be crazy about, can't resist.' Literally 'have no eye for X,' but figuratively reversing the surface meaning — the eye loses its judging function in the presence of the loved thing, so the person can't resist. Common collocations: 甘いものに目がない ('can't resist sweets'), 寿司に目がない ('crazy about sushi'), お酒に目がない ('a sucker for booze'). The に marks the focus of the irresistible attraction. Note how Japanese routinely outsources personality and emotion to body parts (目, 心, 気, 腹) — a productive metaphorical strategy across the whole language.