Businesses, in the U.S., who allow people into thier establishment do so by choice. They can just as easily ask anyone to leave. They can close thier doors anytime they like.
By the very laws governing businesses, they are not "public", nor or they "open to the public". The business owners are free to make that choice themselves. The federal or state governments should not be allowed to have a say in who is, or is not, allowed into a place of business. They very nature of such laws/statutes removes freedoms from the business owner.
Reasonable laws/statutes which govern the safety issues in a place of business are already in place. Adding one which states a business must post as to whether or not they allow smoking is reasonable as it does not restrict the owner of the business and allows the people entering the establishment to make a choice before they enter.
I have no sympathy for non-smokers who chose to enter a place of business which allows smoking. Anyone making that choice should suffer the consequences of that choice. It's not like the business owner forced you into his/her establishment.