NY accommodation in September

Hi, im travelling in Sept to NY with my husband and daughter. I have a bad back injury and am trying to find a hotel where I know the mattresses are supportive/and or relatively new.. also looking for rooms which are very clean/not dusty. Any ideas for which hotels I should try first. We were looking at the library hotel, are you familiar with it? Any recommendations as well on location, its my first visit, feeling a little overwhelmed!! thanks Karen