O.C.G.A. § 16-11-127
(a) As used in this Code section, the term:
(1) 'Bar' means an establishment that is devoted to the serving of alcoholic beverages for
consumption by guests on the premises and in which the serving of food is only incidental to the
consumption of those beverages, including, but not limited to, taverns, nightclubs, cocktail
lounges, and cabarets.
(2) 'Courthouse' means a building occupied by judicial courts and containing rooms in which judicial
proceedings are held.
(3) 'Government building' means:
(A) The building in which a government entity is housed;
(B) The building where a government entity meets in its official capacity; provided, however,
that if such building is not a publicly owned building, such building shall be considered a
government building for the purposes of this Code section only during the time such
government entity is meeting at such building; or
(C) The portion of any building that is not a publicly owned building that is occupied by a
government entity.
(4) 'Government entity' means an office, agency, authority, department, commission, board, body,
division, instrumentality, or institution of the state or any county, municipal corporation,
consolidated government, or local board of education within this state.
(5) 'Parking facility' means real property owned or leased by a government entity, courthouse, jail,
prison, place of worship, or bar that has been designated by such government entity, courthouse,
jail, prison, place of worship, or bar for the parking of motor vehicles at a government building or
at such courthouse, jail, prison, place of worship, or bar.
(b) A person shall be guilty of carrying a weapon or long gun in an unauthorized location and punished
as for a misdemeanor when he or she carries a weapon or long gun while:
(1) In a government building;
(2) In a courthouse;
(3) In a jail or prison;
(4) In a place of worship;
(5) In a state mental health facility as defined in Code Section 37-1-1 which admits individuals on an
involuntary basis for treatment of mental illness, developmental disability, or addictive disease;
provided, however, that carrying a weapon or long gun in such location in a manner in
compliance with paragraph (3) of subsection (d) of this Code section shall not constitute a
violation of this subsection;
(6) In a bar, unless the owner of the bar permits the carrying of weapons or long guns by license
holders;
(7) On the premises of a nuclear power facility, except as provided in Code Section 16-11-127.2, and
the punishment provisions of Code Section 16-11-127.2 shall supersede the punishment
provisions of this Code section; or
(8) Within 150 feet of any polling place, except as provided in subsection (i) of Code Section 21-2-
413.
(c) Except as provided in Code Section 16-11-127.1, a license holder or person recognized under subsection
(e) of Code Section 16-11-126 shall be authorized to carry a weapon as provided in Code Section 16-11-
135 and in every location in this state not listed in subsection (b) of this Code section; provided, however,
that private property owners or persons in legal control of property through a lease, rental agreement,
licensing agreement, contract, or any other agreement to control access to such property shall have the
right to forbid possession of a weapon or long gun on their property, except as provided in Code Section
16-11-135. A violation of subsection (b) of this Code section shall not create or give rise to a civil action
for damages.
(d) Subsection (b) of this Code section shall not apply:
(1) To the use of weapons or long guns as exhibits in a legal proceeding, provided such weapons or
long guns are secured and handled as directed by the personnel providing courtroom security or
the judge hearing the case;
(2) To a license holder who approaches security or management personnel upon arrival at a location
described in subsection (b) of this Code section and notifies such security or management
personnel of the presence of the weapon or long gun and explicitly follows the security or
management personnel's direction for removing, securing, storing, or temporarily surrendering
such weapon or long gun; and
(3) To a weapon or long gun possessed by a license holder which is under the possessor's control in a
motor vehicle or is in a locked compartment of a motor vehicle or one which is in a locked
container in or a locked firearms rack which is on a motor vehicle and such vehicle is parked in a
parking facility.
So from what I gather, 16-11-127 only prohibits firearms in a 'State Mental Health' facility, not any other kind of medical facility, and there is also no mention of banks. The upper sign has the correct designation for the law regarding places you can't carry, I'm guessing the lower sign just transposed a - in place of the 2 as 16-11-1-7 does not exist.
There is no mention of banks and I see no reason you shouldn't be able to carry in a bank.
Signs also do not have force of law in Georgia so you should technically be OK to conceal carry there, but, they are private property and it is their right to deny the presence of weapons if they so choose. And if they ask you to leave you had better comply.