It would indeed depend on the laws in your individual state.
Pretty blanket areas are government buildings: courthouses, schools, et cetera.
Start looking for the no guns allowed signs every where you go.
In some states, signage means nothing. In others, it can be a criminal offense to violate posted (non-government) areas.
In Ohio, posted signs carry the force of law. Meaning that if you knowingly carry in a posted building, you can be charged with trespass, criminal IIRC.
Lots of folks tend to hang their hat on the "knowingly" potion and take great interest in looking at their belly buttons while walking through entrance doors. I don't, I like being armed and would like to keep it that way, ie not having my license suspended - so I assume signage to mean that my business is not welcome. I do not
go out of my way to look for them, however. If I don't see it, I don't see it. If I do, I disarm, have a brief conversation with the manager, and I leave.
I make exceptions from time to time, such as going to the grocery store that is right down the street (posted) for 1 or 2 items versus going across town to the un-posted one.