650K is not going to get you a four bedroom anywhere near a decent school in DC or anywhere within walking distance to bars and other nice things. DC real estate is very disappointing. If you want to compromise on the school district then Petworth will be a good bet for you, still going through a transformation this neighbourhood has a few small bars, a brand new safeway going up, close to silver spring and lots of young families are moving to this neighbourhood, you’ll have to get your children into charter schools.
If you can afford 1.2 million plus in budget, look for west of the park you may get all three things you are looking for.
PS- I wouldn’t necessarily advertise your race. It shouldn’t matter in modern America.