There are many "up and coming" areas in NYC. However, when you say "undervalued" I would say none. New York City real estate is not cheap, but there is a range in prices based upon location. More established neighborhoods are more expensive, neighborhoods that are now becoming popular are increasing in price, but more affordable. My advice would be to work with a skilled, experienced agent who will tailor your search to your needs and your budget.
Halstead Property, LLC
The Upper east side! its a great area here in NYC and seams to give you the most space for your dollar. Give me a call when your in town so we can discuss in more detail. as for up and coming areas in the city I would say just passed Yorkvill right before Spanish Harlem on the fare east side of NYC btw second ave and the river From 99th to 103 -104-105 ish. This area is really up and coming with a lot of new development going on.
Harlem is definitely back on the uprise now, and a great place to buy for future value. I also like Gowanus, Bushwick, Prospect Heights, Clinton Hill, Bedstuy...
It depends what you are looking for in a purchase - would this be a primary residence, or are you looking for a Condo or Multi Family Home for an investment? I would recommend different areas for you depending on what your plans are.
Best of luck, and feel free to reach out.