NYC has so many hotels. They are often expensive and not necessarily in the neighborhoods you would like to explore. The majority are in the Times Square area. Many of my tour clients have booked through Airbnb with great success! You can choose your neighborhood (Greenwich Village, Chelsea, Harlem etc.) or borough (Queens, Brooklyn etc.)
There are also plenty of hotels in Long Island City, Queens that are typically only one subway stop from Manhattan. So don't just look for the best price in midtown. It is of course nice to book a place to stay close to transportation.