If you want something truely amazing you'll probably want to spend more like $1K, with a DAC and amp. At US$350 you'll get really nice headphones, but the source is starting to get important at that level.
I still rate the Audio Technica A900, and if you're in Wellington you're welcome to listen to mine, plus the LCD2. Sony have some decent enough headphones in this price range I think, but they also have some naff ones. Sennheiser 650 perhaps, but they may be out of your price range, they need an amp and the bass is good but not great. Beyerdynamic make some pretty nice headphones too.