I'm also in GA. I'll just give you my opinions. Everyone is going to have different views around here. Just stay legal and do what you are comfortable with doing.
1) Signs have no force of law. Places that are off-limits are simply that; whether they have a sign posted or not.
My response to this is... CARRY THERE. A public establishment has no duty to protect you or your loved ones. Don't care about hurting their feelings by not abiding by their misguided views. Some have mentioned that the owners of these places have "property rights" and you should follow their "will". Well, don't forget that you have your own rights, as well. One of those being the 2A, and your right to carry and protection. If you are asked to leave for ANY REASON and you are carrying, you must do so - or potentially face trespass charges. These are public places who are inviting the public to conduct business. They have to accept the consequences and responsibilities for doing so.
2) Without owner permission, it is illegal to carry in a bar. It is not illegal to carry into a restaurant that serves alcohol. It is also not illegal to consume a beverage and carry your gun. It is illegal to consume alcohol and FIRE your gun.
My response again is... keep the weapon. Eat at the restaurant. Have a beer. Go on your way. Yes, getting drunk and carrying is a really bad idea - albeit not necessarily illegal. Be responsible. However, I do not recommend sacrificing you or your family's safety for having a beer with dinner. This is flawed logic. Again, be responsible. If you can operate your car (a massive deadly mechanical weapon), you can have a lifeless mechanical tool on your hip. It's not gonna jump up and act on it's own. No, I'm not condoning drinking and driving, either. Don't be stupid. Be responsible.O.C.G.A. § 16-11-134
Discharging firearm while under the influence of alcohol or drugs
(a) It shall be unlawful for any person to discharge a firearm while:
(1) Under the influence of alcohol or any drug or any combination of alcohol and any drug to the extent that it is unsafe for the person to discharge such firearm except in the defense of life, health, and property;
(2) The person's alcohol concentration is 0.08 grams or more at any time while discharging such firearm or within three hours after such discharge of such firearm from alcohol consumed before such discharge ended; or
(3) Subject to the provisions of subsection (b) of this Code section, there is any amount of marijuana or a controlled substance, as defined in Code Section 16-13-21, present in the person's blood or urine, or both, including the metabolites and derivatives of each or both without regard to whether or not any alcohol is present in the person's breath or blood.
(b) The fact that any person charged with violating this Code section is or has been legally entitled to use a drug shall not constitute a defense against any charge of violating this Code section; provided, however, that such person shall not be in violation of this Code section unless such person is rendered incapable of possessing or discharging a firearm safely as a result of using a drug other than alcohol which such person is legally entitled to use.
(c) Any person convicted of violating subsection (a) of this Code section shall be guilty of a misdemeanor of a high and aggravated nature.