Look in … Northeast/Capitol Hill (SE)/Eastern Market (SE). Even as far as the Potomac Ave Metro stop.
And yes, a lot of people will tell you it’s a “bad” area, but it’s changed MASSIVELY in the past 10 years, so their knowledge is out of date.
Why not rent something for 3-6 months and wander around the city before jumping into buying? The market is very seasonal, and the fall market will be less hot anyway.