She's been to New York once.

Literal

She [topic-は] once New York [to-へ] went thing exists.

~たことがある ('have done before / have the experience of') is the standard frame for past experiences. It literally reads 'the act of having gone exists,' framing past experiences as nominal facts that 'exist' for the person. 一度 ('one time') here gives a precise count — she's been exactly once, distinguishing this from a casual 'has been' that would leave the count vague. ニューヨーク is a katakana loanword for the city name, pronounced with Japanese phonology (with a long ー). Cities and proper nouns are routinely transliterated this way.