The ancient port city of Caesaria in Israel
Outside the national park, in the modern day neighborhood of Caesarea is the Aqueduct Beach one of the most breathtaking beaches imaginable. With an ancient aqueduct marking the edge of the beach the breathtaking approach is even more stunning up close. There is no lifeguard here so bathing is not strictly allowed although it does get busy on summer weekends, but the site is worlds away from the beaches further south with a more rural surrounding and breathtaking archaeological features.
All this is exploring is likely to get your appetite going, and there are some brilliant restaurants in Caesarea at the Harbor. They vary in price although most are pretty good and serve seafood at an awesome location overlooking the Mediterranean.