This is like asking "what is the best oil for the NSX" or "should I run 10W30" or "what is the best wax"? Those questions never end well on the forum. But, I'll give it a shot.
A 3,000 mile change interval will not hurt your NSX. You are leaving plenty of room for error and you will always have a clean engine. I would not go beyond 3,000 if you are using conventional (dino) oil.
On full synthetic, the problem becomes more the filter life than the oil life. A good full synth can last up to 15,000 miles. But, most filters lose effectiveness around 7,500. Thus, you can just change the filter at 7,500. However, most people change the oil too.
Royal Purple is a good synthetic oil, so I think you would be fine with a 7,500 mile change interval.
Another thing to remember is that many NSXs do not see even 3,000 miles per year. Regardless of mileage, I suggest changing your oil once per year. I usually do mine in the spring so I have clean fresh oil for track season.
Honda, NAPA, Purolator, Mobil and Wix all make good filters for the NSX. I use Denso tall filters, which are the same as OEM. Stay away from Fram.