I think your views of both the Bronx as well as America are pretty distorted.
First of all, the Bronx is quite calm.
Second of all, this graph shows government funding of these places. Obviously NASA gets alot more money than that, but most of it is from private grants/etc.
As for the invasion of places, we don't 'try to run it', we try to put people in power who will support our ventures and allow us to do w/e we want in their land.
Also, if you look at similar pie charts for all countries, it would be rare to find one in which the funding for education is more than the funding for defense.