We had our honeymoon at the Sandals in Antigua. It was amazing! We went during their carnival which is the largest carnival in the Carribean. So much fun! It was considered a holiday and everyone in town was pretty much there for the parade. There were police of course, but I noticed none of them had a gun! Or really weapons in general. It seemed a very peaceful country--very Bob Marley :)
We took an island tour which ended with swimming in the ocean with wild stingrays--amazing! We also did a sailing trip to Bird Island where they cooked us one of the most delicious meals I ever had and we snorkeled. Sandals was great! We ate and drank like Kings and they had fantastic customer service. No tips were accepted, so they did it right because it was their jobs, not trying to kiss butts for tips. The beaches were beautiful, the ocean warm and very very nice people. We can't wait to go back!
Where ever you decide, have a blast!
Oh, and I think our trip was not in that budget--I think we spent $5k on the trip, but we live on the West Coast, so our plane ride was expensive. And of course we spent extra on the activities we did and when we went into town to eat/drink for the Carnival.