Yes, Grove is the place to go for dinner if you have only one night. It'll be a cab ride from wherever you're staying. Make your reservation as soon as you can; they're on OpenTable. The three-course prix fixe, with wine pairings and dessert option, is a bargain.
If you're staying at the JW Marriott and don't feel like venturing outside, six.one.six is very good. It's also walking distance from the Amway Grand.
Let me know where you're staying and I can make some recommendations. (If you want to also do this via a PM, that's OK, too.) I don't think of our having local specialties per se, but there are some interesting options, depending on your food preferences and how much time you'll have available.
GR has become quite a good food (and beverage) town. I love letting people know what we have to offer.