Defense/aerospace, government, and finance (perhaps less so now) are all industries that engage mathematicians. I have personally worked in defense and defense-related industry for my entire (still short) career (think tank, defense university, R&D), and found a great deal of intellectual freedom and interesting work in every job I've had.
The Agency mathematicians with PhDs I've met over the last decade or so are clearly very competent. While I won't speculate on what they do on a daily basis, the people I have met uniformly seemed to be engaged in activity that they found interesting (though at least two have since left to other government posts). They go through an introductory program to teach them relevant techniques and rotate through various offices for a few years to learn the lay of the land. NSA also has affiliated FFRDCs that support internal mathematical research. I have met people affiliated with these as well and they all seem to enjoy the work and to find it fulfilling.
As an aside or two, the field of symbolic dynamics was basically inaugurated by Hedlund while working at one of these FFRDCs, and James Simons (of Chern-Simons and hedge fund fame) is also a well known alumnus. There are many other prominent mathematicians who have worked at or continue to consult for these centers, and if you search CVs you can probably find quite a few examples.
Finally, I would suggest looking at this.