Today's NY Post has a fascinating story about a couple who purchased a 175 square foot apartment in NYC for $150,000. In addition to the purchase price, they have to pay $700 per month in maintenance (For people who have never lived in NYC, the "Maintenance" fee includes taxes, heat, the doorman, etc.) . While not in a horrible neighborhood, Morningside Heights is not exactly the best neighborhood either.
Having had a chance to read the story, I think their solution to living in the city is ingenious (if crazy). For example, they don't keep work clothes at their home. They keep them at various dry cleaners and pick them up on the way there. Because they never cook (very common in NYC), they are not paying for kitchen space they never use. While I don't believe they can live as a couple like that indefinitely, I think they have made a good investment because the Columbia University is located in Morningside Heights. If they need to , they should be able to rent out the apartment for much more than their maintenance fee.