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Of all places, she says she wants to travel to Antarctica.
Literal
She [topic-は] place [even-も] would-be [despite-に] Antarctica [to-に] travel-want [quotative-と] is-saying.
場所もあろうに (ばしょもあろうに) is a rhetorical set expression meaning 'of all places, when there are so many other places she could choose.' あろう is the volitional/presumptive of ある, and に here marks the concessive — 'despite there being (other options).' 南極大陸 (なんきょくたいりく, 'Antarctica') makes the choice dramatically unusual. The whole construction expresses the speaker's amused disbelief.