Howdy,
I'm currently in an instructor billet at NNPTC/NPS. I went through OIS in the summer of 2002. Check out the OIS site (https://www.cnet.navy.mil/netc/ois/) if you haven't done so already.
Before you can take the D.C. trip, you have to take a trip to visit the school in Charleston, SC. This trip is just to give you an idea of what we do here, so you can figure out whether or not you want to be here. If you like what you see, and your application is approved, then you'll take the trip to D.C. to interview at Naval Reactors for the position. You'll be grilled by a bunch of senior engineers, and then Admiral Bowman (Director, Naval Reactors) himself, so you'd better know your stuff. I applied in December 2001, took the physical and NPS trip in January 2002, and took my D.C. trip on February 2002. It doesn't usually go that fast, but you can speed things up by getting all your paperwork done ASAP.
Officer Indoctrination School (OIS) is basically officer training for noncombatants (medical professionals, lawyers, and a small handful of nuclear instructors and design engineers). It's 6 weeks long and most of that is spent in classrooms. You will do a lot of marching and some PT, but it's nothing like OCS. The primary difference is that OCS students aren't commissioned until they finish, while OIS students are commissioned (direct input officer) before they arrive.
Teaching at NPS isn't a bad job, just realize that you won't be considered a "real" Naval Officer until you've been to sea. Most instructors choose to seperate after their 4 year tour. There are opportunities to stay in if you want to (primarily Human Resources and Engineering Duty Officer), but this really isn't the path if you want a traditional Naval career. It's hard to get started in another Naval community (SWO/Subs/Aviation, etc.) when you're already 4 years behind everyone else.
