We spent five days in Antigua at Cocobay Resort in June 2013, and absolutely LOVED it. This was our first experience at an all-inclusive resort, and Cocobay took fantastic care of us. The setting is stunning, set away from the busy St. John's area, so it's quiet and private. The staff was incredibly friendly and eager to help us and answer our questions. We were already talking about returning before we had left!
We had booked a private dinner on the beach for our last night there, and midway through the appetizer course it started pouring. The staff helped move our table up underneath an umbrella at the infinity pool, and tried hard to make things special for us despite the weather. We really appreciated all their efforts.
The only things I would note: There are mosquitoes at night, and the restaurant is outdoors, so pack some bug spray and itch cream. In June, the weather was beautiful some days and scattered showers other days. That said, the rain seems to come and go pretty quickly, and most people just keep on doing whatever they're doing right through it! (Unless it's a downpour.) The scattered showers did not prevent us from thoroughly enjoying our time.
Excursions: The staff plans excursions away from the resort throughout the week. We were able to take a trip one night from 4-8 p.m. to Shirley Heights, an historic area atop a mountain overlooking Nelson's Dockyard. A steel drum band played, and locals barbecued jerk chicken and ribs (I included a photo in this review). Delicious food, and a great environment to watch the sunset. Price: $22/person USD for the taxi, and $8 USD/each for the entry fee at Shirley Heights. We highly recommend this.