Technically on property - just in a non-Disney run resort. It's very nice there. Actually all in the area are great (Il Mulino and Shula's)I'll throw one out that hasn't been mentioned: Bluezoo at the Dolphin. It's very adult-ish. It has a Las Vegas type decor. It's also quieter than most of the restaurants mentioned here since it's off-property and is quite pricey.
As far as food, I'm a big fan of Jiko and Flying Fish which have already been mentioned.