I agree with a previous poster...timing is everything. We have preschoolers with us, and they wake up VERY early. So we tend to lunch early, and eat dinner early, and things are quieter...which is less stimulating to them as well. We all know how overstimulated preschoolers can get at Disney World!
I also recommend Yachtsman Steakhouse at the Yacht Club and Brown Derby at MGM. If you want something less formal than the Steakhouse, there is a bar/lounge next to it that serves appetizers and lighter dinners, and is pretty quiet and cozy. I actually really enjoy this spot.
Coral Reef in Epcot is also relatively quiet. I find the restaurant in Mexico to be noisy and sort of overstimulating myself - mainly, I think, because the tables are so close together. But I've never been there when it wasn't crowded, so I could be wrong.
Haven't eaten at Flying Fish at Boardwalk, but when I've stuck my head in, it looked fairly low key. Also V& A is quiet, but I'm not sure what dining level you're looking for. I fear we're all giving you fairly nice/expensive locales - but with anything less at Disney, you're going to find LOTS of kids, and hence, more noise.
Maybe something at the Swan and/or Dolphin? Swan/Dolphin fans out there?
Good luck, and have fun!
