1)For the State Facility, do you mean in Augusta, if so probably not.. Below is a link to Handgunlaws.us that lists areas around the Capital Area.
2) if the lot is specifically on School Property then no. If it is on a City Street i believe you could be in the clear(But don't quote me, i'm not a lawyer)
3) If you are in the Post Office or the Parking Lot of a Post Office that is Federal Property.
4) You can carry in a bank.
All- if i am wrong on this please Correct me.