I'd either stay by the airport or in the City. Unless I was saving countless buckets of money, or was visiting dead people in Colma, I wouldn't stay in DC. I'd be more inclined to stay by SFO for a morning flight, just so I know I'm there. Although most hotels aren't BART-convenient (except that the airport shuttles take you to SFO, where you can hop on BART, but for a substantial fare surcharge), I'd simply take an Uber Pool or similar to the closest non-SFO BART station, or see what the fare to SF is, which can sometimes be quite cheap.