Great thread - makes me want to go back right now.

Anse Marcel
Grand Case Lolos - Talk of the Town
La Villa
Tropicana
Sola y Luna
Ocean 82 - but haven't tried the reopened one
Friar's Bay Cafe
Sunset Cafe (at Grand Case Beach Club) (dinner better than lunch)
Bacchus - pre Irma - not sure it is open now.