Narita is a problem for long stopovers. Tokyo is too far and expensive to visit even on the train. In Europe, often the city is close enough to get to for under $20. (inside 4 hours)
Gold through Black AMEX (Centurion) card carry some weight. (I have neither) If you have an Elite flyer card it may get you into some respective clubs. (policy varies) I wouldn't expect to get in free alone though, they have a gauntlet of people inside the door to check ID and tickets these days. Since 911, many airports require the check, as arriving passengers must go through security screening. (as well as the clubs defend their turf, else its no longer exclusive) In other parts of the world, you can pay for a day pass. (or priority pass) I don't know about Narita a la day, though I think Northwest sells day passes. You may want to call your airline and see if you can buy a pass.
Another option is to try and meet someone on the plane\Airport who has a membership and slide in as a guest for free. I have done this many times for others. (always seemed like a nice thing to offer to me) You can figure it out by the folks who board the plane early or pester the CSRs for upgrades. So talk to folks near the CSR. Idle chit chat is easy.
I know nothing about day rooms. More familiar with Hotels offering short stays in Airports for a refresh though.
I was there a week ago. I used the United Red Carpet Club based on status cause I always use the showers there. (free inside the club) There is also free wireless access. Showers are available at Narita for $20, I don't remember.
btw- what does NDR mean ?