I think your budget and your preferences for the type of school you want to teach in play a big part in what you're looking for. Before I go any further, let me first state that I don't have children so I can't really speak of DC schools from an insiders perspective. However, I'm pretty sure DC-schools have not been highly rated in too many areas. In fact, there has been a controversial voucher system in place for several years because of the crappy school system.
With that being said, some teachers like to tackle the problems affecting inner-city schools (which I admire), and you may be one of those people. If that's the case, i'm sure the DC school system would welcome you with open arms.
As far as neighborhoods go, your budget and openness to roommates (or not) are certainly things to consider. DC itself is pretty expensive, but the suburbs are a little more reasonable and have more options. Are you dead-set on living in the city limits of DC, or are you open to the "proximity" of DC?