I have stayed in many hotels in the United States and Europe, ranging from luxury hotels to really low budget places. I can honestly say that the hotel Carter is THE WORST of the lot!
Please ignore the room picture that they post on their web site, after staying there I can only qualify that picture as a deliberate scam! When you arrive at the hotel you have to deal with their desk attendants, there is a particular Chinese lady who is positively THE RUDEST hotel clerk I have ever encountered in my life. My room looked like it had been last renovated sometimes in the late 60's, with a renovation cost of maybe $10 tops. The walls were dilapidated and dirty, the carpet completely filthy. The closet had no hangers or drawers to speak of, and it looked more like a very dirty tool shed than a place where you would like to leave you clothes in. The bathroom was a nightmare. The TV remote didn´t work, there were no lamps, and the bathroom light was broken. The bedsheets were torn and the whole room had a musty, unpleasant smell.
When I tried to reason with the lady I mentioned above, she repeatedly tried to walk away from me. After I stopped her a couple of times she pointedly told me that they did not cleaned the rooms or changed the towels. After a heated discussion she gave me two towels (I refused the first she gave me because they were fithy and had burn holes in them), and a light bulb for the bathroom that I had to change myself.
I would have gladly walked out and tried another hotel if my stay hadn´t been paid for in advance.
When I returned home and set out to write this review, I was further apalled to discover the horror stories from other guests (or victims?) of this place.
Do yourself a favor and NEVER book this hotel. New York is a great city, and staying there shouldn´t have to be a nightmare. There are other options in the budget end for Manhattan hotels that provide at least a minimum of cleanliness and comfort.
If you decide to contemplate the Carter (for whatever reason!) at least read beforehand the New York Post articles of  August 31, September 1 and September 2 of 2007, that describe the dead body of a young woman discovered under the bed in one of the rooms by a maid!