One of the typical problems in another country is the names of the food.
The Sandwiches
Personally, I like sandwiches of all kinds, chicken, mashed potatoes, fried eggs and mushrooms. Luckily Israeli cuisine includes an intense focus on sandwiches with chicken, fried eggs and mushrooms as well as mashed potatoes as a side.
The Hebrew word for "sandwich" is כָריך "karikh" ("kh" is pronounced like German "ch"), from the verb לכרוך "likhrokh", "to cover".
What is covered includes "chicken", in Hebrew "3of" עוף (the 3 is a voiced pharyngeal fricative, imagine something similar to a voiced <h>). That word derives from the verb לעוף "la3uf", "to fly" (without a device). It really means bird but is generally used for chicken. The actual word for chicken (male) is תרנגול "tarnegol" and for chicken (female) תרנגולה "tarnegola".
Typical items to add to the chicken sandwich include בצל קלוי "batsal qalui" (the "ts" is an emphatic <s>), "onion roasted", מלָפְפון "melafefon", "cucumber", פטריות "pitrioth", "mushrooms", singular פטרייה "pitriya", "mushroom", גבינה "gvina", "cheese" (this non-kosher combination exists in Israeli cuisine but not in traditional Jewish cuisine).
Another typical topping for a sandwich is ביצת עין "bitsath 3ayin", "egg of an eye", "fried egg". It can be called ביצה מטוגנת "bitsa metugeneth", "egg fried", as well. Note that ביצת "bitsath" is "egg of" followed by a genitive while בצה "bitsa" is just "egg" followed by an adjective. לטגן "letagen" means "to fry". Also possible is a חביתה "chabitha", "omelette".
Of course Israeli cuisine often ignores the difference between foods based on meat "basar" בשׂר and milk חלב "chalav". A kosher restaurant would not be able to offer both in the same room or made in the same kitchen.
Kosher Kitchen
Kosher-related terms include
כשר "kasher" = "fit", in Yiddish כשר "kosher" = "kosher" (apparently Soviet Union Yiddish used the spelling קאָשער)
בשרי "basari" = "meaty" or "meat-based", in Yiddish פֿליישיק "fleishik" (this word was apparently deemed kosher by Soviet Union authorities as it included no Hebraisms)
חלבי "chalavi" = "milky" or "milk-based", in Yiddish מילכיק “milkhik".
פרווה "parewe" = "neutral" (not meat-based and not milk-based, includes fish and, originally, birds), in Yiddish פארעווע "parewe" (this word is actually of Yiddish and perhaps ultimately Slavish and not Hebrew origin)
טרף "taraf" = "prey" (meaning meats that come from aninmals that either are animals of prey or have become prey to one), in Yiddish טרייף "treif" (treif things cannot be eaten legally in any combination)
One food that is very typical for the entire levant from Egypt to Syria (and apparently was invented by Christians for lent-based meat fasts) is food based on chickpeas. These include חומוס "hummus" and פלאפל "falaafel" (the א Alef used to mark the long vowel is a sign that this word is of Arabic origin). Hummus is typically eaten with טחינה "tachina", a kind of sesame sauce.
For those who want to eat meat, a typical food in the entire region is the kebap (in Turkish, pieces of meat), called שווארמה "shawaarma" in Arabic and Hebrew (again the א Alef marking a long vowel).
And then there is garlic: שום "shum" in Hebrew, תום "tum" in Aramaic, and ת׳ום "thum" in Arabic. Add it to anything, all the time.
My personal favourite is מרק עדשים "maraq 3adashim", "soup of lentils". (Apparently the Arabic term is שורבת אלעדס "shurbet al3adas", "soup of the lentil", with "shurbet" meaning "soup" and deriving from the word "to drink" שרב.)
Never mix meat and milk in the same food or kitchen.
Potatoes and Related Evils
Other typical toppings for sandwiches are חסה “chasa” = “lettuce", עבגנייה with an Ayin “3avganiya” = “tomato", and sweet potato בטטה "batata", coming to Israel via Arabic traders who travelled without the letter "p".
As for the potato per se, it derives its name, like many things do, from the word for apple תפוח "tapuach" (not the one from Genesis, that was a פרי "peri" which is the source of the word "pear" and very likely was one such, as pears are the apple relative native to the region). A potato is a תפוח אדמה "tapuach adama", "apple of earth" or "apple of ground", and an orange is a תפוז "tapuz", originally a תפוח זהב "tapuach zahav", "apple of gold". Eat them with the linguistic ramifications in mind.
There is an entire garden of linguistic riddles involved with all the words for fruit and earth. פרי appears related to all sorts of growing things, like פרה "para", "cow", while אדמה, "earth" or "ground" is related to אדם "adam", "man", and דם "dam", "blood", as well as אדום "adom", "red". Think about what this means regarding "be fruitful" פרו "peru" and other parts of the story.
It just adds to the general confusion that the word for "mashed potatoes" is פירה "pire" from French "purée" via German and Yiddish. The word is of course unrelated to fruit and cows.
If you are sick of drinking milk, you can have מיץ "mits", "juice", יין "yayin", "wine", or מים "mayim", "waters" (which is plural).
For those who prefer restaurants over streed food, let it be known that "restaurant" is מסעדה "mis3ada", from לסעוד "lis3od", "to dine". "Food" as such is אוכל "okhel", from לאכול "le'akhol", "to eat". And לשתות "lishtoth" is "to drink".
To order (and to invite) is להזמין "lehazmin" and you can pay using כסף "kesef", "silver" or "money", or כרטיס אשראי "kartis ashrai", "credit card".
The Grains and Meats
Jewish bean counters have an entire book on what to do and not to do with which types of grains. And they actually did include beans in those regulations.
The word for bread is לחם "lechem" and the typical grains are חיטה "chita", "wheat", דורה "dora", "millet", שיפון "shippon", "rye", אורז "orez", "rice", and תירס "tiras", "maize". אפונה "afuna" is a bean or a pea.
Certain grains must not be eaten in a leavened state during Passover. Find all relevant regulations and traditions on the Chabad Web site Passover section.
Israel is located in the world's wheat zone. All other grains are traditionally imported but some, like rye and millet, have been known for millenia. The word for rice came with the rice.
Apart from עוף, the bird, typical animals to be eaten include בקר "baqar", "beef", טלה "tala", "lamb", and the Turkey bird הודו "hodu", which is “India”. It is named, like in England, after a far away land. Note that Turkey is not far away from Israel but India is. Also note that the damn bird actually comes from America.
Note that rye is very prominent in European Jewish cuisine but not in Israel. I don't know if rye actually grows in Israel very much. Generally Israeli cuisine is not close to Ashkenazi (German-Jewish, European-Jewish) traditions. The שניצל "shnitzl" made it over as did some other "delicacies" but most Israelis don't eat them (and no sane tourist would want to).
Israel, as a country culturally bordering Germany, is capable of producing some great chocolate as well. But that is a tradition that came to Israel from France and Austria and it's not native.