http://www.no-smoke.org/pdf/ecigslaws.pdf
Here is a list of places which partially or totally ban e-cig use. However how individual businesses interpret a no-smoking ban may go beyond these specific regulations. It would seem however that if the legislators felt a need to add e-cigs to the existing anti-tobacco regulations there is an implied belief that anti-smoking rules did not automatically include anti-e-cig coverage. In the list you will see that Marion county Florida bans e-cig use in places where smoking is prohibited.
County passes restrictions on e-cigarettes | Ocala.com
It is a tricky and interesting question whether the reasons for the anti-smoking bans should apply to vaping. There are no documented second hand inhalation issues, there is no actual smoke. There is a visual simulation of cigarette smoking, there may or may not be long term health issues for the user in nicotine addiction. But we don't ban use of other nicotine delivery systems, gum or patch, in public spaces. And we don't ban the use or carrying of steamy odor producing products, cup of coffee.
So can a restaurant tell a diner not to vape? Being a private business it may regulate the behavior of customers in any way it chooses and does not need a law to permit such regulation. You must wear a suit, no outside food or drinks, no shirt no service, are all examples of rules the restaurant makes up and enforces.