answer: nowhere. There aren't any places in Strasburg where you can get a VA state safety inspection for your car. (a valet service that takes your car to Front Royal for a fee to get your car a state safety inspection doesn't count.)
this can be quite a problem for those who live alone.
Strasburg is a town that's known for antique vendors. Strasburg is what it sells--an antique.
Strasburg residents: The closest VA state safety inspection that I could find is Anchor Automotive in neighboring Middletown (tiny when compared to Strasburg). On their website https://anchorautomotivellc.com/ Anchor claims "no wait" VA state safety inspections. I found this to be the case.
It's better than nothing. But then, what do you expect from a town that's known for being an antique?
attribution: Gary Cope and Flickr