Nice to hear about this.
Using a 2009-2011 Stock GTR for Super Street Class SCCA autocross-
The OEM runflats are OK and better than many other non runflat tires, of the options, the OEM Dunlop SP Sport Maxx GT 600 DSST CTT is the fastest (on track) and can be mounted on both front and rear OEM wheels using stock suspension which I would think is the best option. However in 285/35-20 there are three versions, each with slightly different tread depth and tread designs:
Year Front Size Rear Size
255/40RF20 (97Y) 285/35RF20 (100Y)
2013 8/32" 9/32"
2014 7/32" 7/32"
2014 NR1 6/32" 7/32"
For standard version for 2009-2013 MY GTR in 9/32" tread depth tirerack.com has it listed for $516 each, 39 lbs, 200 treadwear for all 3 versions
For 2014 GTRs or later in 7/32" tread depth, $549 each, 38 lbs
For Nismo GTR (NR1 version) in 7/32" tread depth, $583 each, 38 lbs, (front tire size is 6/32" tread depth)
You can also use the Bridgestone Potenza RE-070R or RE-070R 2 in 285/35-20, 140 treadwear, they cost less and also have different tread depths, 8/32" for the R2 (40 lbs, $467 each) and different tread design. RE070R is $485 each, 39 lbs, 9/32" tread depth, tread pattern is less aggressive.
For better wear you can use Dunlop SP Sport 7010 A/S DSST (ultra high performance All season tire), 240 treadwear , 10/32" tread depth, 40 lbs in 285/35-20 $520 each. The tread design is not for performance/track type driving so grip will be less but durability will be better and will last on street longer than the runflat summer tires.
Expect the runflats with 7/32" tread depth or less to perform better for track or autocross but when combined with street use they may wear quickly.
For Non runflats you can again use 285/35-20 front and rear, this will help a little to reduce understeer from providing more front grip.
Extreme Summer tires:
BFG g-Force Rival $305 each, 4 rib tread design, 30 lbs, 200 treadwear
Hankook Ventus R-S3 version 2 $298 each, 31 lbs, 200 treadwear
Goodyear Eagle F1 Supercar
G:2 about $244 each, asymmetric directional tread pattern, 29 lbs, 220 treadwear, tires different for Right and Left sides of car.
Additionally, the GTR may be eligible for Super Street R class (use race tires)
For R compound tires in that size-
Toyo Proxes R888
285/35-20 on front wheel, $378 each, 31 lbs, 100 treadwear
315/30-20 on rear wheel, $418 each, 33 lbs.
Or
Nitto NT-01 Road course track tire, comes in three sizes, 100 treadwear
255/40-20
285/35-20
315/30-20
All are OK for the GTR.