For those who were wondering exactly what the new law says, I have the information. The website below gives the complete detailed amendments that will take place to the current laws. Below, I have quoted the relevant parts:

www.azliquor.gov/assets/documents/sb1113.pdf

4-229. Licenses; handguns; posting of notice

A. A PERSON WITH A PERMIT ISSUED PURSUANT TO SECTION 13-3112 OR WHO
MEETS THE CRITERIA SPECIFIED IN SECTION 13-3102, SUBSECTION D, PARAGRAPH 1 OR
2 MAY CARRY A CONCEALED HANDGUN ON THE PREMISES OF A LICENSEE WHO IS AN
ON-SALE RETAILER UNLESS THE LICENSEE POSTS A SIGN THAT CLEARLY PROHIBITS THE
POSSESSION OF WEAPONS ON THE LICENSED PREMISES. THE SIGN SHALL CONFORM TO
THE FOLLOWING REQUIREMENTS:
1. BE POSTED IN A CONSPICUOUS LOCATION ACCESSIBLE TO THE GENERAL
PUBLIC AND IMMEDIATELY ADJACENT TO THE LIQUOR LICENSE POSTED ON THE LICENSED
PREMISES.
2. CONTAIN A PICTOGRAM THAT SHOWS A FIREARM WITHIN A RED CIRCLE AND A
DIAGONAL RED LINE ACROSS THE FIREARM.
3. CONTAIN THE WORDS, "NO FIREARMS ALLOWED PURSUANT TO A.R.S. SECTION
4-229".

B. A PERSON SHALL NOT CARRY A FIREARM ON THE LICENSED PREMISES OF AN
ON-SALE RETAILER IF THE LICENSEE HAS POSTED THE NOTICE PRESCRIBED IN
SUBSECTION A OF THIS SECTION.


C. IT IS AN AFFIRMATIVE DEFENSE TO A VIOLATION OF SUBSECTION B OF THIS
SECTION IF:
1. THE PERSON WAS NOT INFORMED OF THE NOTICE PRESCRIBED IN
SUBSECTION A OF THIS SECTION PRIOR TO THE VIOLATION.
2. ANY ONE OR MORE OF THE FOLLOWING APPLIES:
(a) AT THE TIME OF THE VIOLATION THE NOTICE PRESCRIBED IN SUBSECTION A
OF THIS SECTION HAD FALLEN DOWN.
(b) AT THE TIME OF THE VIOLATION THE PERSON WAS NOT A RESIDENT OF THIS
STATE.
(c) THE LICENSEE HAD POSTED THE NOTICE PRESCRIBED IN SUBSECTION A OF
THIS SECTION NOT MORE THAN THIRTY DAYS PRIOR TO THE VIOLATION.


D. THE DEPARTMENT OF LIQUOR LICENSES AND CONTROL SHALL PREPARE THE
SIGNS REQUIRED BY THIS SECTION AND MAKE THEM AVAILABLE AT NO COST TO
LICENSEES.

E. THE SIGNS REQUIRED BY THIS SECTION SHALL BE COMPOSED OF BLOCK,
CAPITAL LETTERS PRINTED IN BLACK ON WHITE LAMINATED PAPER AT A MINIMUM WEIGHT
OF ONE HUNDRED TEN POUND INDEX. THE LETTERING AND PICTOGRAM SHALL CONSUME A
SPACE AT LEAST SIX INCHES BY NINE INCHES. THE LETTERS COMPRISING THE WORDS
"NO FIREARMS ALLOWED" SHALL BE AT LEAST THREE-FOURTHS OF A VERTICAL INCH AND
ALL OTHER LETTERS SHALL BE AT LEAST ONE-HALF OF A VERTICAL INCH.


F. THIS SECTION DOES NOT PROHIBIT A PERSON WHO POSSESSES A HANDGUN
FROM ENTERING THE LICENSED PREMISES FOR A LIMITED TIME FOR THE SPECIFIC
PURPOSE OF EITHER:
1. SEEKING EMERGENCY AID.
2. DETERMINING WHETHER A SIGN HAS BEEN POSTED PURSUANT TO SUBSECTION A
OF THIS SECTION.

4-244. Unlawful acts

31. FOR ANY PERSON IN POSSESSION OF A FIREARM WHILE ON THE LICENSED
PREMISES OF AN ON-SALE RETAILER TO CONSUME SPIRITUOUS LIQUOR.

4-246. Violation; classification

C. A PERSON VIOLATING SECTIONS 4-229, SUBSECTION B OR 4-244, PARAGRAPH
31 IS GUILTY OF A CLASS 3 MISDEMEANOR.
http://www.azleg.state.az.us/ArizonaRevisedStatutes.asp
Here are the penalties (from the above link) for violating the above statute (class 3 misdemeanor):
13-802. Fines for misdemeanors
C. A sentence to pay a fine for a class 3 misdemeanor shall be a sentence to pay an amount, fixed by the court, not more than five hundred dollars.

13-707. Misdemeanors; sentencing

A. A sentence of imprisonment for a misdemeanor shall be for a definite term to be served other than a place within custody of the state department of corrections. The court shall fix the term of imprisonment within the following maximum limitations:

1. For a class 1 misdemeanor, six months.

2. For a class 2 misdemeanor, four months.

3. For a class 3 misdemeanor, thirty days.

*****

It is worth noting that this new law lowers the penalty from a class 2 misdemeanor to a class 3 misdemeanor. The law also references "concealed handgun" meaning you cannot conceal other firearms (rifles/shotguns) nor can you carry openly. There is no A.R.S. anywhere to be found that prohibits the carrying of non-firearm weaponsin on-sale liquor retailers (bars and restaurants). You can still openly carry knives, batons, pepper spray, tasers, and pellet guns for instance. It is reasonable to assume that an establishment may choose to prohibit those as its private property rights. It is also worth noting that the law requires the sign (at least one of the signs if there are many) to be placed directly next to the liquor license. I'm sure the establishment could still reserve the right to ask you to leave (as its private property rights) even if not properly posted but you could not be cited per that section if it is not properly posted.

I am not a lawyer but that is the interpretation I got. A lot of these signs have been going up lately and I have yet to actually see one placed where it is supposed to be (next to the license). In that case, if you are not drinking and concealing and are keeping your mouth shut about carrying, you should be legal despite the signage since the signage is not meeting the requirements of the law. It is also worth noting that class 3 misdemeanors are generally considered very petty crimes by police and courts. I believe that driving 20 mph over the posted limit or littering on the highwaysare class 3 misdemeanors. You are likely to be cited and pay a fine but it is unlikely you would have to do jail time. Again, I am not a lawyer and I don't know how any given court would rule if you break this new liquor law but if they treat it like other class 3 misdemeanors, you may be looking at little more than less money in your wallet and a slap on the wrist. I will not advocate breaking the law but if you choose to, you know what the most extreme consequences are ($500, 30 days jail).