From everything I have read posted by people who actually do open carry in Virginia on a regular bases, Virginia is similar to Washington in their acceptance of open carry - it's perfectly legal and 99% of the population won't notice, or won't indicate that they notice and you will have very minimal issues, and I open carry 99% of the time in WA. So, for me personally there is no need to conceal the gun HOWEVER....
While I do not like having to obtain a permit, I have my Washington CPL and I would advise you to obtain the VA permit for a couple of reasons:
Federal law prohibits you from carrying a loaded firearm (openly or concealed) on public property within 1000' of a school unless you have a license issued by the same state that the school zone is located in. That applies in Virginia as it does in Washington (and all the other states). So that is reason #1, if you wish to comply with the Federal law and not have any concern about it ever being enforced.
I don't know if VA is the same, but the CPL in Washington state makes it legal for me to carry in a couple of places that would be illegal without the permit. For example, again in WA - on school property when picking up or dropping off a student. Yes, I open carry when I do that; no, it has never been a problem. Also in WA, in stadiums and convention centers owned and operated by municipal governments I am exempt from firearms prohibitions they might have with my CPL.
Unlike VA, I have to have a CPL to keep my gun loaded inside a vehicle.
So... I would also advise to obtain the VA permit, just to stay legal in some instances and if you decide to conceal the gun, it gives you the option to do so.