Depends on the type of engineering, if it's software or building related there are jobs in NYC.
If you are an electrical engineer or mechanical engineer or chemical engineer or aerospace or nuclear, etc... there are probably a total of 5 or 6 of these hired in the entire city on a given year if that. The exception is research jobs at the universities.
You're going to find that tech companies like to be about an hour outside of cities like New York or Boston on cheap land in the burbs. 90% of the jobs in New York are finance related or legal work for finance, etc... Then you have everyone in the service industries trying to support the finance companies. Financial firms can basically print money and thus can afford 10 to 100X the rent of companies that actually make stuff.
This fortunately may change in the near future. Google recently moved Motorola into the city of Chicago from the burbs. NYC has planned a technical campus on Roosevelt island and startups are starting to get it that innovation is more efficient when it is done in the core of a city.