Most of the places you can't carry are govt. locations, both local and federal, the post office or places that post a sign saying that they don't want weapon on premise.
It used to be that you could not conceal in any place that serves alcohol but, that was repealed years ago. You can conceal at dinner if you don't drink.

It is mostly common sense. I just got up so i may have left some locations off, I am sure others can fill in any gaps I might have forgotten about.

Are you going to be visiting any specific places?

Also, we have no duty to notify if you encounter a police officer. I know N.C. you have to tell the officer you are carrying, not sure if S.C. is like that but, i figured i would put it out other.

ETA: i forgot you can can carry on any school property. You can carry in the parking lot as long as you do not get out of the car. This is used more for dropping off and picking up kids.

Signs don't carry any weight of law in Virginia but you can be charged with trespass if they ask you to leave and you don't.
Here's a more complete resource:
VCDL Virginia Carry Info

I keep hearing people say that.  But then the link you gave says "Private property when prohibited by owner (§18.2-308.01.C & trespass violation)"

Note the citation of the concealed carry statute AND the ampersand sign saying trespass violation.

Your concealed carry permit is not valid where prohibited by the property owner.  If you don't have a valid permit then you are in violation of §18.2-308

I've had two attorney's, one of whom was a VCDL counsel and is now a judge, tell me that, in their opinion, you can be charged with a violation of §18.2-308 (class one misdemeanor for first offense) if it can be shown that a reasonable person would have known that carry was prohibited on the private property.  However the one that did a little bit of research could not find any case where a permit holder had ever been so charged.

Since you'll be in Cville, UVA does not allow carry on campus. John Paul Jones Arena, off limits also. Virginia ABC stores have signs posted. The signs are supposed to be obvious and able to be seen but there is no legal size/shape/color. I don't see a lot of signs around town. BW3 at Barracks Road Shopping Center used to have a sign as I remember. I don't usually think to even check for a sign.