I live in DuPont Circle and can tell you right now, your odds of finding a safe area to live in with good schools is probably not going to happen for under 500k. The public school system in DC is absolutely terrible. Hell, last summer I lived across from a crack dealer down at 10th and G in NE, a rowhouse back in that area just sold for 350k and they're tearing it down and turning the block into luxury condos i think.
Your best bet would be a 2br townhouse in Northern VA, it's kind of a crappy commute, but VA public schools are unbelievably good. Chantilly, Centreville, Fairfax, Arlington, Alexandria, etc. Those are all good places to check out for housing. Even then, expect to spend around 350-400 if you want to buy.
If you do want to live in the District, AVOID AT ALL costs anything in SW or SE. Someone has been shot or stabbed to death every weekend since I moved here last August. It's startin to get worse in NE too. Some guy got shot in the face and stabbed 3 times a few weeks ago and someone has been robbing people at local ATM's.
If you want to know about specific areas in DC just send me a message.