Israel has a big variety of food and is very vegetarian friendly.
Here are some chosen ones:
Soups: yemen soup - soup spiced with hawaiej (a mix of spices) comes with meat (or without) and beans. Usually eaten with a loaf of bread or lahuh (another yemen bread), on the side with vegetables and hilbe,(ground and foamed furegreek)
Tahini - ground sesami making a very oilly sauce like amazing seasoning for everything including salad and tooth paste to maintain solid and white shinny teeth.
Hummus - delicious chick peas ground and mixed with tahini. Cream like texture can be put on bread, pita bread etc... In hummus rest you will get a big plate with mushrooms, cooked chick peas, broad bean or meat, as your choice with few pitas, salads, boiled eggs and falafel.
Falafel - comes in a pita with hummus, salad, pickeled cabbage, chips, etc... With tahini, amba (pickeled mango sauce), hot sauce, It is grounded chick peas deep fried in ball shapes (obviously many recipe).
Shawarma - comes in pita or a thick, large tortilla made out of flour with same additions as falafel. It is a turkey meat (the more popular) or lamb (taste better IMO)
Sabih - comes in pita, just like falafel only the main dish is fried eggplant instead of falafel.
Shakshuka - basicly fried onion and garlic, slowly cooked with tomatos till they take all their jucw out, then break whole eggs on top to keep the form till they are cooked with the undirect heat.
Some people add meat or cheese, but that is the basic great one.
Desert: go for druzian sweets - kak, kra, habisa, sahlab, kadaif, baclauwa - all very sweet and (but) very good.
Also a nice druzian "snack" or street food would be druzian pita (slightly different, much more tasty than the regular one) with labane - a sour cream cheese. Perfect.
Those are the popular meals you will be able to get in restaurant almost in any town (exclude the desert and soup).
Yet there is much more food you can get in israel that is associated with specific ethnicity (LIKE the druzian sweets or yemen soup) and they are all so very good.
But you will excuse me for not putting them down...