Open Carry is common and very well accepted here. You will find the occasional business that doesn't allow open carry e.g.: applebees, Chipotle, some malls, (and my favorite pub/restaurant just put up a no gun sign -- sad day.) I have never been bothered while open carrying in Arizona. You are more likely to get asked what you are carrying rather than why. And for clarification for bars: you must have a CCW, you must not drink, you must conceal, and there has to be no no-gun sign -- and it should be next to the liquor licence. That is really the only major restriction in Arizona, otherwise -- open carry and now concealed carry are allowed without a permit, though LEO's appreciate it when you have one.
One tidbit to add... The requirements that are listed for carry into a bar are for ANY establishment that serves alcohol for on-premises consumption. That would include Applebees, Chili's, Chipotle, etc. The prohibition to carry openly in these places is effective wether or not they have signs up prohibiting firearms. As stated above though, if concealed, you aren't drinking, and they don't have a sign up next to the liquor license prohibiting firearms, carry away =)
Sidetrack: Some debate the legality and morality of carrying in cases where a business is posted as being 'no-firearms.' The general consensus is that 'concealed means concealed' in those cases, and that it's only a problem if they ask you to leave and you refuse to do so. My stance on it is that if they're posted, I have no desire to FORCE them to take my money, and will shop elsewhere or not carry there. I also still argue that AZ trespass law is worded in such a way that carrying in spite of such signs would qualify as criminal trespass in the third degree...
http://www.azleg.state.az.us/search...File=/ars/13/01502.htm&CiRestriction=trespass
13-1502. Criminal trespass in the third degree; classification
A. A person commits criminal trespass in the third degree by:
1. Knowingly entering or remaining unlawfully on any real property after a reasonable request to leave by the owner or any other person having lawful control over such property, or
reasonable notice prohibiting entry.
2. Knowingly entering or remaining unlawfully on the right-of-way for tracks, or the storage or switching yards or rolling stock of a railroad company.
B. Criminal trespass in the third degree is a class 3 misdemeanor.
I've seen this argued in both directions, and realistically, if you carry concealed into the average business (let's just say a local mall that is posted) you are pretty much guaranteed NOT to get caught, in trouble, asked to leave, or otherwise have any issues. To each their own on this one =)
That said, alcohol serving establishments are a whole different ballgame as discussed further up and in previous posts, so don't confuse the two.