Very nice hotel, wonderful suites, very quiet rooms, luxurious!
I stayed here for 2 nights to see how this hotel fared in comparison with other hotels that I had stayed at on other business trips to New York City (e.g. The Muse, The Soiftel, etc.). I decided to try one of the Suites on the 11th floor. The Suite I had included a hallway, a large living room, and a bedroom that has the most unique photograph over the king sized bed that actually acted as a nightlight--during the day it was illuminated and at night you could lower the lighting to a low level or not at all. 
The room was quite luxurious; the bed was very comfortable; there was a large walk-in closet with a safe; there were robes (but no slippers); there was a mini-bar (but the ice was on the 2nd floor and you had to ride one of only 2 elevators to get there.
It was a very nice stay but there seemed to be some shortfalls. When I arrived by limo there was no doorman to open the doors or to assist with unloading or getting into the hotels. This was automatic at all my previous stays at the other hotels. I had to go inside and ask for assistance. Each time I came and went in and out of the Algonquin over the two days, there was never a door man to open or close the doors. This was automatic at the other hotels. When the bellman took me to my room on check in, he told me about the ice machine on the other floor (2nd floor) and that I could go get ice if I wanted to and that there was a coffee station there as well (which was a nice feature). But in other hotels, the bellman always went and got ice for me. Even at a Courtyard Hotel by Marriott the bellman went and got ice for me.
So these were some of the minor blips on the radar that caused me to rate this a 4 instead of a 5 star hotel. Also I felt that the bar prices were over the top. $ 24 for a side car or a martini is a bit excessive even in New York City.