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.
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.