In Secaucus, the hotels are near a shopping mall with restaurants and shops, and transportation into the city is convenient. Mike's personal favorite is the Hampton Inn , which provides a free continental breakfast. And a New York City bus stop located just across the street. You can check the prices and availability at Secaucus hotels or book your reservations directly through this link. There are some Bed and Breakfast establishments in New York City.
Apartments are also very expensive in the city.
You can find short-term vacation rentals through several agencies, but they may not be very economical.