A restaurant can simply ask you to leave if they think you are dressed inappropriately irregardless if you're sitting inside or outside or out of plain view. There is no law on how you should dress though is there?
That is only half correct... They MUST have it published, in clear view, to be legal or enforceable. Otherwise it is discrimination. By sign, or contract, or public notice.
SIGN: "No refunds", for instance... is fine, but certain items and services are still subject to a refund, even with a sign.
SIGN: "Dress code...", must be present, or you may frequent within the dress-code of the law. (For restaurants, shoes/sandals, shirts/blouses, and pants/skirts required.)
SIGN: "No Jews", obviously not enforceable even if posted or not posted, on public property. (On private property, like a home or non-business, this is allowable. But not in any public or private business.)
Private business, is one which has no public access, such as a road-paving company, bridge-repair, landscaping, construction contractor. If it has a public-access area, it is a public business, and public property. (For liability reasons and for law reasons.)
There is one exception to the rule... "Private Clubs", which are "Limited public access". They can impose specific limitations that are beyond the scope of public business law. Such as, they can allow smoking inside, and drinking, and stripping, and gambling, with the adequate permits.
When you register with the state/government as a business, you agree to "Public sales law", and "US currency law". You will not refuse service to anyone, without just cause. You will not refuse US currency for any reason, for "All debits public and private", as indicated on US federal bank-notes.
Failure to follow those, and other "Business" rules, is a violation of US policy. You are given the right to sell, using US currency, if you follow those rules.
Businesses are not their own kingdoms. Private businesses are not "Private sales", as they must sell to the public, which requires "Public access", which requires, "Public space", thus, making the sale-area, "Public property".
There are things a business can, and can't say, enforce, do, and not be breaking the law themselves. (Just because they do it, does not justify the actions. Civil infractions can be handled on the spot, by any individual, but can only be enforced by an officer of the law, and can only be tried by a judge in the event of question.)
Once these e-cigs become more understood, and accepted, you will see new laws form, or more public knowledge of what you can't enforce with these products. (It will take years before these can rightfully be banned like cigarettes. However, it could take years before these are accepted as "Not-smoking", as long as visible smoke-like vapor emanates from them. That is the other reason I dilute with distilled water... less vapor seen, and more nicotine in my mouth.)
Also note... non-gated business driveways and parking-lots, are "Public access", areas also. If you speed, you can get a ticket on private property, while driving on a private-drive that is not-gated. This is what makes it legal for employees and delivery vehicles to use them without fear of being arrested for trespassing. However, a private home-driveway, without a gate, is private property, and this is why delivery vehicles do not have rights to enter the driveway, except in emergency, or with permission through contract. (However, if you fall and hurt yourself... you must sue the private owner, for faulty or neglectful care of the public access drive. Should that be the case. EG, you would not sue the state for being hurt on public property.)