Bar none, this is the best located affordable property in the city. Across the street from the New Museum, The Bowery House is in the heart of trendy Nolita and steps away from the Lower East Side and Soho.
Originally opened as The Prince Hotel in 1927, the hotel was reconfigured in the 1940s to serve as the temporary lodging for soldiers returning home from World War II. All floors of The Prince Hotel were rebuilt with single room cabins that were just large enough for a bed and storage of essential items.
Note that the space is SMALL with no windows in the original cabins. This is ideal for those who value location as the most important part of their stay. If you are a heavy sleeper, a single traveler, and don't mind using ear plugs or being woken up by the alarms of about 20 other occupants in your confined space, you will be fine.
That said, the bed is comfortable (and there is no way you will be able to sneak a guest into your very tiny cabin. It's prohibited.)
I would recommend getting a group of friends and splitting a dorm room with them.
Do make sure to make use of the amazing astro turf patio on the rooftop. It's quite incredible and offers views of the World Trade Centre as well as the New Museum.
For value for location, this is your best bet.