Actually there are a lot of banks where carry (open or concealed) is just fine.
One point to keep in mind (we're talking strictly Virginia here folks) is that there is no statute/law regarding firearms on private property. So if a property is posted "no guns" and you carry there anyway and are noticed then all that can -legally- happen is that you will be told you are "Trespassing" and be asked to leave (unless you are violating some other law). If you do not leave immediately then the charge on your rap sheet will start with "Trespassing" and go from there. (this does not, of course, apply to the restrictions on Federal buidlings, schools, etc. where there are applicable Federal laws).
That is the -legal- ramifications. However in the real world people overreact, officers don't always know the law, private security oversteps their authority, situations escalate and on ad infinitum.
In short if a place is posted I simply recommend that you don't go there if you have a choice, or you obey the sign and disarm if you have to enter (like a hospital).
"The dogs may bark but the caravan moves on"