I go back far enough!
I lived in Georgetown in the early 1980s and occasionally visited Georgetown University Shop next to 1789 (but preferred the Chevy Chase location-great selections of shirts for use with black tie), I think I visited Brooks Brothers and J Press 1x or 2x during my time here, but spent most of my funds at...BRITCHES of GEORGETOWN! Once Mark Russell, the great political comedian, called me "a hit man from Britches" when he was performing at the Shoreham (Casper Weinberger, then Secretary of Defense, laughed loudly).
I worked at The Georgetown Inn for some time, and Alan Flusser stayed a few times (his collection was sold at Britches), and Alexander Julian also stayed when his shop opened on Wisconsin Avenue (he drove from New York in his personal Checker Cab!). I do remember Arthur Adler, I think next to Charley's Crab on Connecticut, and of course Raleigh's, Neiman Marcus, Woodies, Garfinkel's (the only place to get Hermes ties in the DC area). And yes, I remember Jos A Banks in its heyday, and even saw Alexander Haig shop there when he was Secretary of State!
As for women's stores (for my female friends, not for myself) the stand out was Saks Jandel, both at the Watergate (near Gucci in my recollection) and in Chevy Chase.
I would say that there is a good selection of trad clothing available here, but I really do miss Britches as its selection was well edited and really spoke to me more than any other store in New York or DC.
Clearly, TKI67, you bring back memories!