Yes While they may be privately owned, are public places and there is no reason to endanger the health of those who choose not to smoke.
For comments "Just go to eat / work elsewhere," not everyone has the luxury to choose non-smoking environment for working or eating, especially bars and restaurants to choose to maintain a smoking area available. Keep smoking and even foreign non-smokers, who, with a lot of people go to health or to save money, get rid of damaged businesses as a place to smoke.
I personally do not like to go anywhere when I know I am going to shower and wash my clothes after. Cigarette smoke permeates everything, tissue, skin and hair, and because I am not a smoker, I prefer not to smell like one. http://answers.yahoo.com/question/index?qid=20120321232656AAMK0KI