I seek the wisdom of ya'll city folk

See... I need to go to the big smoke and I'm horribly inadequate at city driving/navigation/parking/etc.
I need to get to the New Zealand Embassy, which is located near the National Zoo.
So I'm wondering if you have any advice on how to accomplish such a feat? I'm fairly sure I can get to the New Carlton metro station without much issue. Beyond that, I'm pretty clueless. Maybe it's easy to drive to the zoo? It does not look easy btw

Here's where I'm trying to get to:
37 Observatory Circle, NW
Washington D.C. 20008
Thanks
Jim