Back in the days before maniacs flying planes into buildings, you could go up to NETC and get a visitor's pass. My mom took me up one day, and I walked onto the quarterdeck at NAPS and proceeded to spend the next 3 hours chatting with the guy on watch. All kinds of good info was received.
Sadly, since 9/11 no one can visit NETC without a sponsor who is stationed there. Even I, as a NAPS alumni, was not allowed on.
If you want to visit, the best bet is to contact NAPS and ask to speak to the Platoon Commander of the platoon which will have the duty the day you visit and request an escort. Whether you get one will depend on the person you call and how you ask. Aside from calling and asking for the CDO, I don't think you have many alternatives.