The Algonquin Hotel is a wonderful, historic hotel close to everything but very quiet.
My daughter (age 19) & I stayed for a weekend (2nights) of Broadway shows. Being very familiar with Manhattan, we did not want to stay in Times Square -- too crowded, too noisy! We chose the Algonquin for its reputation and location -- on 44th Street about two blocks from Times Square, but in another world crowd and noise-wise.
Yes, the rooms are small, but that adds to the hotel's charm. It IS an historic hotel, built in 1902 -- rooms were much smaller then. We were really only there to sleep and shower and breakfast.
Our room and bathroom were spotless and the room service quick and courteous.
We would definitely stay at the Algonqun again and recommend it wholeheartedly!