Israel is a land of immigrants; Jews came from across the globe after WWII and brought with them a tremendous variety of cuisine. So food they eat in Israel is varied and Israeli food dishes span the globe. You can find excellent Tunisian, Moroccan, Yemenite, Russian, Ethiopian, American, South African, Indian and many other food types through out Israel, including of course Middle Eastern food associated with the Arab countries of their origin.
Of course you will meet falafel and Shawama on every corner, and it has to be tasted. Then there are the less obvious choices. Generally I would say there are a wider variety of meat restaurants than milk, and being a Jewish country many restaurants are Kosher, and so separated into either meat or milk eateries, and closed on Shabbat. In summer try the delicious Israeli fruit, especially water melon. If you are in Eilat or Tiberius don’t miss a Denis fish grilled, and smothered with garlic butter. Why not try the popular Israeli breakfast – Shakshuka – eaten through out the day, it is a mixture of tomatos and eggs.
The foods you must try are falafel, Shawama, humus, tahina and schug/harif/chili paste, all of these you can find at any falafel or Shawama stand.
Apart from these foods try the Moroccan couscous with a vegetable soup on top, and the Yemenite malawach which is a circular flaky pastry served with grated tomatos, cheese and a boiled egg. Even more delicious is the malowach when served as “fatut” which basically means all cut up and messy. Fatut is a malawach cut up and mixed with honey, nuts Cinnamon and raisins, absolutely mouth watering.
I would skip the Japanese, Chinese and Indian foods in Israel; sorry to say I haven’t found any that quite meet international standards.
Then there is the European Jewish staple of gifilta fish, also not something you should go looking for, but I suppose it is a matter of taste. But try the Hungarian goulash or other homey European hot pot type meals.
When Israelis sit at a beach side, restaurant the standard items ordered are chips/French fries, salad and humus as well as perhaps a selection of savory pastries stuffed with meat, these are called cigarim, as they look a little like cigars!
Because the Jews came from around the world after the war there is an amazing selection of food choices, so try as many of the foods they eat in Israel as you can.