Sorry I didn't see this topic until now, but the replies you've gotten have provided very good advice. I'll try not to repeat what's already been said.
Several different kinds of tires have been mentioned in this topic, and they are very different in fundamental ways. I'll use the Tire Rack's terminology for their "performance categories":
a.
Maximum performance summer tires (Continental ExtremeContact DW, Goodyear Eagle F1 GS-D3) last longer (more miles) than the next category ("extreme") and are somewhat quieter. They offer excellent performance, although they are not as sticky as the extreme tires. They are a great choice for someone who is looking for a balance between longevity and stickiness.
b.
Extreme performance summer tires (Dunlop Sport Z1 Star Spec, Yokohama Advan Neova AD08, Kumho Ecsta XS) are the stickiest street tires you can buy. They won't last as long as the previous category and they can be somewhat noisy. The Star Spec and AD08 are very similar to each other in performance; the XS offers similar performance on dry pavement but is significantly worse than the Star Spec and AD08 in rain.
c.
Competition tires (Nitto NT01, Toyo Proxes R888, Toyo Proxes RA-1) are designed for racetrack use, and I don't recommend them for the street, due to a combination of high cost, short treadlife, poor grip in rain, etc.
d.
Ultra high performance summer tires (Dunlop Direzza DZ101) offer nowhere near as much performance as the maximum performance summer tires. They are designed to offer a blend of economy (low purchase price) and performance, and may be a good choice for an inexpensive sporty car like a Civic Si. But I would not use them on an NSX - especially since they're not all that much less in price than the significantly superior Continental ExtremeContact DW.
Now, on to the specifics...
These wheels are both 17's... I heard the TCS may not like a non staggered wheel set up.
That's simply not true. The TCS depends on the outer diameters of the tire sizes to operate properly, and the wheel diameters really don't matter. The TCS will operate just fine with 215/40-17 and 255/40-17 on any year NSX.
Are you saying that the OEM tire was superior? Do you have any suggestions of tires that are better?
The OEM tires (Yokohama A022H and Bridgestone Potenza RE010) were designed specifically for the NSX, and are unsurpassed for handling "feel" and precision. However, today's extreme performance summer tires offer better grip. See above for examples.
As a note Discount Tire will price match anyone. I went online to Tire Rack for these tires and even with shipping, Tire Rack price was better by 10/tire. I told this to Discount, and they matched it, no questions asked.
By all means shop around. And don't forget to make it an apples-to-apples comparison of bottom lines, including shipping (free at local dealers and Discount Tire Direct), sales tax (applies by local dealers but not usually on mail order sales), and mounting and balancing (sometimes free at local tire dealers, otherwise typically $10-30 per wheel/tire).
I've found that, in general, Discount Tire Direct (their internet mail-order arm) is usually slightly cheaper than Tire Rack. Local dealers (including Discount Tire's "bricks and mortar" shops) may or may not be able to equal mail-order prices; it's easier for them to do so in a state with low or no sales tax since that's where they are typically at a disadvantage.
I don't think you have said what they will be used for/what you're looking for in a tire?
Peak performance - dry grip - wet grip - longevity - tire noise - track rat - occasional track use - daily driver - importance of comfort, etc...
Very true. This will determine which of the above performance categories you ought to concentrate on.
You have to do an alignment when you get a new set of tires? And you said settings... as apposed to the hammer I see alignment places use to pound the car into alignment? Can any alignment place do this or is it specialized work?
As noted above, you don't need to do an alignment when you get a new set of tires (although you
do need to do one when you change suspension parts). However, if you haven't had an alignment done in a few years it's not a bad idea. Also note that there is one alignment setting that plays a role in tire wear - the rear toe, which affects the rate of treadwear on the rear tires. (Front tires normally last 2-3 times longer than rears so they are less of an issue.) When the NSX was first introduced, 6 mm of rear toe was recommended, which offered very precise handling but led to rapid rear tire wear. A few years later they changed the recommendation for all NSX years to 4 mm rear toe, which extended rear tire wear accompanied by a very slight degradation in handling feel. Some NSX owners are willing to trade off even more handling feel for greater tire treadwear in the rear, and are using 2 mm or even 0 mm of rear toe. Your car, your choice.
. BUT the price is not the same, in fact it's quite the premium especially if you buy several sets a year. The difference between the two tires is minuscule. Some tests show the Z1 ahead and some show the A08s. 
