I hate (I mean detest) the USA Today and almost always get them, it seems. The WSJ usually is downstairs if I want it but the USA Today is always right there outside of my door. So finally, I decided to put on the comments section of each individual reservation "NO USA Today. Local and/or Wall St. Journal only, or no paper at all." The first reservation I did this with was at the Westin St. Francis. To my surprise, yesterday morning, I opened the door and the WSJ and local SF paper was sitting right there. I was very impressed (I rather assumed many of those comments or requests weren't read much) that my requests were read and honored.

All of this to say: if you don't want the paper, I'd list it in the comments/requests section when you book online. My request worked for me!