I really can't say enough good things about North Arlington. To me it has the best of all worlds - green space, parks - but also has city features ("urban villages" Ballston, Clarendon, Courthouse, Westover, etc) and is close to downtown.
Arlington used to be part of the District, that is why it is in the "square," but you don't get the extra local income tax, with the marginal schools and the lamentable local government.
We absolutely love living here for the past several years - really the best of all worlds.
There are many great neighborhoods. You can find something in your budget, it may not be the most pristine, but something you could be happy with long term.
I also like the advice of waiting a bit -- 1 BR is enough(!) A baby doesn't need too much space.

Think about where you really want to live, and buy when certain. Enjoy everything!