The National Parks at Masada and Caesaria are both open on Shabbat. For more information please see:
Caesaria: http://parks.org.il/ParksENG/company_card.php3?NewNameMade=45&from=116&CNumber=855319
Masada: http://parks.org.il/ParksENG/company_card.php3?NewNameMade=46&from=116&CNumber=853401
Enjoy your trip.