WOW! No need to add any additional suggestions after that gem! Just kidding...
If you want to stay on the island, the best of includes:
- Cafe Boulud - Probably thought of as the best by most - French-American
- Cafe L'Europe - I haven't been, personally, but it has a great reputation
- Bistro Chez Jean-Pierre - people seem to either love it or hate it so dine at your own discretion
Since you're staying at the Breakers you may want to check out some of their restaurants. I believe there are around 10 choices, all upscale, and I've never heard a bad thing about them.
IMO, Cafe Boulud is the only place in Palm Beach worth going out of the way for. I obviously haven't been to all on PB, so my opinion is somewhat on hearsay and reputation. Off the island, however, there are some staples that you'll see consistently on the boards. I would make the 20 minute drive up to Jupiter for either Food Shack or Leftovers Cafe (same owner, same concept, similar menus, just that busy to have two).