Good thread. I'm in a different car (90k mile NA2 pop up targa, owned for 2 years), occasional track use. Came through RX7, Ford GT and AM V8 Vantage roadster.
Engine sound - standard sounded ordinary to me: there are some great aftermarket units that release a bit of power, reduce weight (you won't believe how much the OEM silencer and cats weigh!) and sound much better. You won't get your extra 50HP but maybe 15??
Steering - to my mind it's the weakest element of the car. Innovative when it was launched but it's not class-leading. There's always a little bit of guesswork involved in - for example - coming into a roundabout or taking a sharp corner. Predictability has improved since I swapped for Type-R suspension, but this isn't everyone's cup of tea (although my dentist is loving it). It's also prone to understeer in the wet on the harder suspension so you pays your money and takes your choice.
6 speed - I've never shared your thoughts and others have said that the earlier 5 speed was a better box, so maybe it's me! BTW changing the standard knob to a Type R one improves the shift sensation by shortening the shift gait. Coupled with a Type R mesh boot it looks better too. There's someone selling Type R knobs in the USA on eBay for $78 - genuine NSX-R ones have yellow lettering but are $$$s more.
Brakes - standard ones are fine for road use, but put them on a track and they are seriously wanting. I swapped mine for Powerslot slotted rotors and they are much better, with no downside as far as I'm concerned.
But overall, mine is a joy to own and drive. I think the secret is it's lightness (notwithstanding the OEM exhaust...) - this imbues the car with a deft touch that more powerful metal just cannot match. A mate owns an AM V8 Vantage N400 - on the straights he blows me away but come to corners and it's the other way round. I know which I enjoy more.
Daily driver: Jaguar iPace HSE
2000 NSX Coupe, Circuit Blue, was W2NSX now V6NSX
Renault Megane RS Trophy R
Other interesting mode of transport: Bell JetRanger