Long winded response:
A while back (more than a year, less than five, if memory serves) I had a lengthy and friendly discussion with a DoD attorney about the firearms regulations and general federal law, military facilities/properties, VAs, and even post offices.
Following is my recollection (be advised that I’ve told my wife that my memory has become unreliable enough that I’m planning soon to stop using it for anything important):
Military properties: 18 USC 930 applies in general and, indeed, applies to buildings in which government business is being transacted. Carry on military property otherwise is under the strict purview and absolute control of the facility commander and has the force of law within the confines of the facility.
VA: She told me they have their own rules, including no firearms in the parking lot, regardless of state law to the contrary, and that these “rules” have actually occasionally been tried (don’t have any cites) and the courts have upheld the VA’s right to do what they want in this regard. In short: No firearms allowed anywhere on VA property including in your vehicle in the parking lot.
Post Office: 18 USC 930 applies and the Post Office also has the right to prohibit firearms in their parking lot (as long as it is their parking lot). They do not have control over guns in shared common parking lots where the Post Office is, for example, one of several tenants of a property.
To the best of my recollection, we did not discuss Federal Court buildings, but I believe that it’s simply application of 18 USC 930 and parking lots don’t enter into the matter.
Please understand that this was one DoD attorney who, despite the fact that she assured me she knew what she was talking about; 1) Maybe she didn’t and 2) It is possibly now outdated information.
Things can change and YMMV.
A personal account:
Several years ago (coming on ten now) I was employed by the DoD on a military base. I routinely carried firearms in my vehicle which fact was known to the powers that existed on the base, up to and including the Wing Commander and there was not a problem.
A couple of Wing Commanders later, I had occasion to revisit the issue with the NCOIC of the Security Group who informed me that he would obtain a “permit” for me from the Wing Commander. Within the hour he called me back and informed me that it was not going to happen and that, henceforth, no such latitude would be allowed for anyone.
I am currently working inside a VA facility (as a DoD contractor: I do not work for the VA) and I am convinced the VA police will briskly, if not vigorously, enforce the no firearms policy anywhere on their premises.
Best wishes for a happy Thanksgiving.