。
She left her family behind and went to New York.
Literal
She [topic-は] family [object-を] behind [in-に] leaving New-York [to-に] went.
後に残す means 'leave behind,' literally 'leave (someone or something) in the back.' The に on 後 is locational, not directional — the family stays at the back of her trajectory while she moves on. ニューヨーク is the standard katakana rendering of 'New York'; for many Japanese the city is the iconic American metropolis, an aspirational destination for art, business, and cultural ambition. The sentence has a clean narrative ring to it, suitable for biography or fiction.