June Honeymoon Recommendations?

Does anyone have any recommendations for where to honeymoon in June? My fiance and I were thinking about going away for a week, most likely to an all-inclusive location. Our budget is around $5k, not really interested in staying in hostels or going on a cruise. We would be leaving from O'Hare and would like to leave the country, we're open to any destination as long as there is no snow haha. When we travel we like to keep busy, zip lining, wine tours, visiting museums, etc., so we would like a destination that has a lot to do. Would appreciate any help on this!