I would draw a 1,000 foot circle around the White House, and Congress, along with the memorial areas....and that’s as far as you should consider SAFE. I spent 3.5 years there....leaving in the summer of 2013. I even walked around the Anacosta area, and the east side of town...which are definitely no-go areas after dark.
For a six by six mile area....it’s thug-city, with these few federalized zones where cops are in abundance.
It wasn’t all that long ago that 13th was a no-go area. “Capitol Hill” is bigger than it used to be! Which, is good.
Also true is that a whole lot of the people living there have a direct line to the media, so any complaint gets local and federal attention. (I moved into an even tougher neighborhood a few years after the riots. We had to work hard for that publicity, but we got there. It makes a difference.)
Lanier and the police in DC are really good. There always bad apples in the transitional areas, and when they are taken down, things clear up in the (good) neighborhoods for a good part of a year. Then there new muggers. But fewer than years before. “Gentrification” is a process, not something that happens and is done.
I’ve lived here all my life, and you’re right about that radius around the most predominant tourist sites.