I really like our neighborhood, kalorama Sheridan. Free standing houses go from near $4mm to $8mm. It is as close as you can get to downtown (10 minute walk), but still feel exclusive. Grand homes and at that price point you fit in with everyone else. Great neighborhood park, extremely safe and pretty streetscapes.
We looked a bunch in Cleveland park, which is a fantastic neighborhood, but home prices are generally $2mm -$3mm and not as exclusive. It is also not as close to downtown, but it is a great neighborhood.
There are some houses in Georgetown, which some people love. Houses vary from $1mm to over $10mm. They vary in scale and luxury too. I lived there in law school and it is not for me at this point in my life, but it is cute.
Personally I would avoid some of the outer neighborhoods, but there are very small pockets of houses in your price range in forest hills, Cleveland park, spring valley, weley height and mass ave heights.