We took that cruise earlier in the summer. We only can speak of one place to eat as we were too busy enjoy the snorkling and beaches and such to bother stopping at a restaurant.
On Antigua, grab a cab and ask to go to Church Beach (Also called Nest Beach). The beach is unbelievable and there is a great little bar/restaurant called "The Nest" that serves very reasonably priced drinks and has a BBQ from which they will make you food if you wish.
On Dominica go to Champagne reef if you like snorkeling. There are a couple of restaurants near the ship area but we did not have time to eat.
Carnival Cruise Lines:
Fantasy 90, Celebration 95, Victory 05, Conquest 05, Spirit 6/06, Freedom 6/08, Holiday 7/08, Victory 6/09, Valor 9/09, Dream 6/10, Splendor 8/10,Conquest 8/11,Magic 11/11,Triumph 4/12,Spirit 7/12,Freedom 11/12, Triumph 2/13 - The fire cruise, Magic 1/14
NCL Dream October 2006, RCCL Mariner OTS June 2007, Celebrity Silhouette 2013