Perseverance - The fast-paced lifestyle, seemingly gruff attitude of residents, and noise and smells of this big city (home to 8 million people) are not for the weak of heart. The New Yorker must know how to stand up for him or herself in different kinds of situations.
Frugality - New York is one of the most expensive cities, cost-of-living-wise, in the world. Knowing when to scrimp and save, and when to go all out, will help the New Yorker have fun and still pay the rent.
Sense of Adventure - Hey, that's why people move here, right? Go out to see new neighborhoods, different restaurants, galleries, the whole nine yards.
Self-sufficiency - It will help the new transplant tremendously if they learn how to use public transportation, how to read subway maps, how to take new routes, when to call the landlord (and how many calls it takes to get him to come over), how to eat dinner for less than $5, etc.
A love of New York - No, it's not a necessity. But it could help!