Greece for our honeymoon

Hi everyone, my soon to be husband and I are planning our honeymoon and want to start in Greece (and stay about 5 days before going to another country). We haven’t been before and are not sure where to start and what the must-sees are, so any recommendations would be lovely! We love eating together, going site seeing, and learning more about the culture (we tend to stay away from super touristy places)

We would also love recommendations on where to stay (not super expensive but also true to the greek experience!)

Thanks in advance 🙂