Recommendations for honeymoon Greece private pool

Hi there!

I’m looking to book a honeymoon for September 2026. We would love to visit a resort or hotel for 2 weeks with:

-adults only -possibly all inclusive -we would love a private pool with our room -budget 7-9k (without flight)

Does anyone have any good recommendations? We are not familair yet with Greece, so we have no preference for the place where the hotel is. There are sooo many options when searching online. I would love to hear experiences from other (honeymoon) travellers!

Thanks!