I do agree with you on the private property. My "applause" was for the banning of smoking at public beaches.
Private businesses should be allowed what to do what they want. The patrons who either come in or don't come in to said business will tell the business owner what his/her policies should be. If a restaurant allows smoking, and nobody eats there because of that policy, the business owner should probably make it no smoking.
Then again...he/she might have the only (or one of the few) restaurants in town who do allow smoking and all the smokers go there; and the business is successful.
Public places are different. Beaches, parks, etc. I have no problem with a ban on smoking in public places.
Private business is entirely different. The government doesn't need to dicate to private businesses on their smoking policies. The profitability (or lack of) will do that for them.