No, the real issue is what the NSA is doing. They're reading my damned mail, listening to my calls
Yes, and how are they doing that? Because you're using easily-tapped electronic forms of communication. If you were sending your messages via sealed scroll (presumably with something more modern than wax) you might have greater informational security. And indeed, when corporations or even simply savvy humans want to communicate, that's precisely what they do. The data gets bundled up and handed to a courier, and if security is sufficiently important, they will literally drive it to the airport, get on the plane with it, take it to another country, and hand-deliver it so that you have a reasonable expectation that there has been no eavesdropping.
Or, you know, you could just use encryption. But they'll still gather metadata. But then, they can do that regarding the travel related to your package. There's always going to be some kind of wrapper, even if the only one they get to read is your itinerary, gathered retroactively.
How do I "not use" the NSA?
Move out of the country, become a citizen of another nation (tricky if there's not a baby on the way) and renounce your US citizenship. Then, don't use electronic communications :)