What better way to the heart of a country than through its stomach? How about it?
Besides experiencing the culture, sample the food.
Since Judaism is Israel's majority religion, its precepts inform much of the country's culture, including its cookery. Much of said cookery will be "kashér" (more commonly rendered in English as kosher), from the Hebrew for "fit," as in stipulated fit for consumption by religious texts. The best-known such stipulation is the prohibition against mixing meat and dairy (you might notice this especially at breakfast, where you'll see plenty of milk-derived products but no bacon, sausages, and the like). So do stop into a kosher restaurant or two during your stay - for example, any one of those located on downtown's Shenkin Street. It's an especially yummy way of getting to know yet another facet of this country!