Once I switched my search to nearby areas the hotel rates dropped immensely and I was able to find a nice chain hotel offering rates that were about half of what the 1 star hotels were going for in the city. I ended up booking the 2 rooms I wanted for 7 nights and I was very pleased with my choice. We didn't end up staying in a trendy boutique hotel in the heart of NY but our rooms were clean and we were able to afford a 7 night stay.
Our hotel offered a free airport shuttle which was very convenient since we weren't familiar with the area when we first arrived and our room had the basic amenities like a fridge, large television and even a microwave which we used for late night snacks. We got up early each day to head into the city and by the time we got back at night we were so tired from sightseeing that we didn't even care that we weren't staying in a luxury hotel. It might seem nice to say that you're staying in a fancy hotel, but at the end of the day all that really matters is that your room is clean and you have a nice place to sleep after a long day.