From New York to… where?

We are planning on honeymooning next year (wedding is this Christmas but we don't have time for a honeymoon then). We are from the UK and want to fly to New York for a week's city break then fly to somewhere for a week lounging by the sea doing very little other than accepting cocktails and reading books. 🙂 We would fly home from that part of the trip.

Looking at the map, we could probably get to Mexico or the Caribbean fairly easily, though wouldn't be averse to flying further. The main thing is that we don't want to inadvertently end up in tropical storm country.

We could go in April or end July-August. Which would be better and where would you recommend for our second week?