Best honeymoon option in the Caribbean?

Hello, my fiancée and I are looking to stay ~10 days in the Caribbean for our honeymoon in early June. We are hoping to keep expenses under $5,000 and want nice beaches (preferably not too crowded), as well as some scenic hiking. We have been looking at Curaçao, St. Kitts, or St. Lucia, and are having a tough time deciding. Any insight on the differences between these islands or hotel recommendations would be much appreciated!