Caribbean Island Recommendation for honeymoon in late June

Hi everyone

I am getting in mid June and going on honeymoon with my wife-to-be on around the 22 June for two weeks. We plan to spend a week in New York and then fly to a Caribbean Island for a week. Can I please get some recommendations on which to pick.

Our budget is reasonable, but not limitless so we’re looking for somewhere that is sensibly priced where we can also relax but have access to a good amount of activities too. If some people can please recommend some places I would very much appreciate it! Not sure if the time of year is less than ideal to go there because of hurricane as I read June is a bad month for them potentially. We will be getting there right at the end of June. Thank you!