OK going to feel old here.
Armor Jacket: Available in a wide selection of tailoring, from chic street styling to the harsh ribbed and padded aesthetic of macho mitiliarism, these jackets offer substantial protection. - Shadowrun 2nd edtion.
Later the "Secure Line" of armor came along, you had Secure Jacket, Secure Longcoat and such they were a little more expensive than the basic stuff but they were much more concealable. Mind you this is still in the 2050s and 2060s (don't quote me on that, going mostly by memory and see the start of the post).
In my mind, as technology started to move towards nanites and spidersilk I would think that the older, more obvious forms of armor have fallen into disuse. The actioneer business suit for example offers really good protection and still looks like a business suit.
So maybe like this:

Or like this:
