I'm a bit unsure because I didn't find that usage on Google.
She came back to New Work out of nostalgia for Mark.
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While that's absolutely fine grammatically and technically fine semantically, it's probably not the word you're looking for. Nostalgia, while it can absolutely be for a person, isn't usually felt for a person.
Perhaps you meant that she missed Mark? Without context we can't tell. If you're sure nostalgia is what you mean though, the sentence is fine.