I was in your exact situation two months ago, deciding between an automatic or manual NSX. I had never in my life driven a manual, which made it all the harder to choose.
After a LOT of thinking, we decided to buy the 6-speed, and I am VERY VERY glad we made that choice. While the manual is more "work" to drive, it is very fun work, and I simply don't drive it under conditions (lots of stop and go commuting) in which an automatic would be much better.
Advantages to the manual:
1) CONTROL!!! Being able to shift from 6th to 3rd, etc.-- and being able to use the clutch to exert fine control over the car's movement
2) FUN FACTOR-- There is something viscerally enjoyable about going through the gears in my opinion
3) POWER-- 290 vs. 250ish HP is a significant difference
Disadvantages
1) Manual is more work to drive
2) Clutch is not 100% flawless 100% of the time, and will eventually need replacing
3) Under certain conditions (stop and go commuting, lots of upwards hills), manual can be a pain to drive.
Overall, I would strongly advise getting the manual, and learning to drive stick if you don't already. When I'm tired or worried about stop and go traffic, I simply don't drive the NSX (nor should I).
-David ('01 Silverstone 6-speed)