As explained to us in my CCW class (http://www.lsp.org/handguns.html#prohibited), the Class A-General retail permit is a business that has more than 50% of their sales based on alcohol consumed on the premises (i.e. a bar or nightclub). Restaurants do not have a Class A license. Neither do liquor stores.
I carry daily into restaurants all across the city. This was explained very carefully in the classroom.
Edit: However a church, synagogue, mosque or similar place of worship is in fact OFF LIMITS.