We stayed 5 nights at Villas Mlini. Conveniently located between the airport (15 min by car) and Dubrovnik (15 min by car) . Absolute paradise!!! The villas are fantastic, calm and with direct view over Mlini Bay. The facilities of Hotel Astarea are quite ok, nothing fancy since this is an old hotel, but everything was in very good shape. The outdoor pool and garden are in fact very posh, everything maintained and clean. The breakfast at Hotel Astarea offers everything you want. Just a few minutes walk are the boat haven (with regular ferry service to Cavtat and Dubrovnik; if the sea is calm), a few local restaurants (which offer very nice local cuisine), some cafes etc. If you have kids, there are a bunch of very nice playgrounds in 5-10 min distance walk.
Check-in etc is taken care at hotel Astarea, so tell your driver to go there. They might not know "Villas Mlini". We arrived already early in the morning and despite check-in time is 15:00, the villa was ready for us.
No need to tell about nature and the water. This is probably the best Europe has to offer.
Anyway, it cannot get better, we will definitely come back.