The LFA interior is really sweet, especially with the color changing digital tach. Unfortunately the car does not handle as well as I believe the actual car would. I am a big fan of the Ferrari Scuderia (interior is beautiful, and it is one great car to drive).
Of topic but.. HUH? The LFA is one of the best handling cars in the game, and thats without even doing anything to the suspension...
And on topic:
The NSX-R has a cool interior, and handles fantastic (if you like lift off oversteer, which I do) - not sure why some are saying its a cheap car; one of the fastest online around 500pp.
LFA, also super cool interior
Any of the newer Ferrari's - 458 is currently my favorite car - not the fastest non-race car in my garage at 600pp, but certainly close - but the noise, the handling, the shifting, and the interior - very easy to drive very fast.
S2000 - tuned properly, it's a beast (if you want an actual beast, the Amuse S2000 will kill most anything this side of a full on race car, and even then...), I think I'm using a tune from RKM that I modded a little bit - very, very quick (it's light), cool interior, but obviously will be lacking horsepower on longer tracks.
And if you like the Si, try the Integra Type-R - again, with a proper tune, its very fast, light, and has those cool white faced gauges.
Best view out? Mclaren F1 - but that seems a tad bit overkill from what your asking for. Is amazingly fast though, albeit "tricky" to drive quickly.
And you can't go wrong with a '12 GTR; not a great interior (imo), but certainly the workhorse of the game - does everything well, even rally (yep, try it).
