I am getting married 30th June and have booked our honeymoon on 2nd July to Mexico for 2 weeks. We have never been to Mexico before but have travelled to many places in the Caribbean (Jamaica, St Lucia, Barbados, Antigua, Dominican Republic) all during the months of May - September.
They do say that the rainy/hurricane season is during the months of May-October but if a hurricane is going to occur it is usually during the later month of October. As for the rain, well, of all the places i've been to it has hardly ever rained and if it does it down pours for about 10 minutes and then the blue skies come out again.
Honestly you can't go wrong in the Caribbean, it is not like England where it rains all day every day like I said the most you'll get is a down pour for 10 mins and then blue skies again.
Of the places that I have visisted I would say the following:
St Lucia is beautiful, just stunning, it is like a picture postcard everywhere you look and the people are so friendly, loads of site seeing and tourist activities, very safe to just walk around and the hotels are gorgeous. (visited 4 times)
Dominican republic is very hotel based not much going on outside. (visited 1 time)
Jamaica is a gorgeous country full of culture and good vibes, the people are very friendly and there is loads of site seeing to do. (visited 3 times)
Barbados is beautiful, gorgeous seas, friendly people, but not a lot to do with regards to site seeing. (visited 2 times)
Antigua is stunning, the sea views are amazing, but a very relaxed holiday, not much site seeing and very hotel based. (visited 1 time)
Wherever you choose in the Caribbean you will have an amazing time.