I know they do say that they have non-smoking rooms. I've always stayed in one. And am currently booked in one for my next trip. Perhaps they are not coming up because they are all booked? However, keep in mind, like in Europe, even the very best of non-smoking rooms still have a hint of smoke scent. It's just the way it is. It generally bothers me for about ten mins and then I can't smell it anymore.
Just came back from Sheraton. When you check in, they will double check whether you want the non smoking room. Someone in the other mail thread about the age is starting to show, but my room was excellent! Got upgraded to the family room w/ 4 beds as a SPG member.
I had the same problem with the online Hilton website: for a month or two it would not allow you to choose a non-smoking room. I just called Hilton directly to make my reservation and it wasn't a problem.