I'm not a constitutional expert, but I fail to see how regulation of commerce (that is, regulation of the money-taking newsracks that hold newspapers) represents a violation of the First Amendment. No government official is telling the Tennessean or the City Paper what it can or cannot write. The proposed Council provision is only providing limits on the lengths to which publications can go to receive money in exchange for their writings. It is also re-couping a percentage of the money that newsracks would otherwise freely save just sitting on public property. Newsracks are commerce and they should be taxed for their upkeep, unless they are on private property.
The mainstream print media would not be in this hot water right now if they were more neighborhood-friendly and worked with associations (like Downtown's Urban Residents Association) to come up with workable solutions to the long lines of plastic and metal newsracks that clog some Metro sidewalks. But businesses, especially corporate businesses--and given the influential economic ties between corporations and governments, I have to laugh when I hear the former complaining about their rights being endangered--do not self-regulate. They simply do not. They generally ignore the problems they cause for others, unless citizens organize to lay those problems back at the feet of business.