I don’t think a $200 a night hotel is what it once was.
I used to get rooms at Best Western etc. in the $50-60 range even in New Orleans and then that edged up to $80 (and more with tax) and even $117 etc.
Short notice booking can sometimes get you a better rate and other times full fare.
When I stayed in Green Bay WI (casino) and Brooklyn NY (Holiday Inn) it was upwards of $200 a day/night (about a decade ago).
For that price I doubt they are in DC but probably in Prince George’s County in MD or Baltimore