Unless otherwise posted, you can carry in restaurants. Not if they serve alcohol, though.
Not true, there is a new law. Carry in restaurants that serve alcohol and bars is legal as long as they don't post and you cannot consume alcohol while carrying. There is a specific sign that has the ARS # on it that must posted to keep you from carrying.
Check out http://www.arizonashooting.com/v3/
and look for all the threads about this new law.