I once had a Jewish classmate. She told me that when she celebrated her bat mitzvah, she would have gone to Israel with her family, but she couldn't at the time, because there was too much war. Is there a Jewish custom to travel to Israel for a bat mitzvah? Is there some custom to visit there at least once in a lifetime? Is Israel the Jewish mecca (it's a pun)?
Judaism doesn't have a current pilgrimage obligation the way I understand that Islam does (I believe every Muslim is required to go to Mecca once). However, Israel and, more specifically, Jerusalem is very important to Jews; Israel is our homeland, and Jerusalem is the site of the temples (past and future). Further, Jerusalem used to be a pilgrimage obligation three times a year when the temple stood, as commanded in Devarim 16:16. (See also Pilgrimage Festivals at My Jewish Learning.) So it is not surprising that Jews prioritize Jerusalem as a travel destination even if we can no longer go to the temple. According to Ketubot 111 one who walks four amot in Eretz Yisrael merits a place in Olam HaBa (the world to come) (h/t @sam). Some also hold that we are obligated to move to Israel if we can.
Synagogues, Federations, and other Jewish groups organize tours, and Birthright subsidizes trips to Israel for college-age students. While these groups sometimes organize trips to other destinations of Jewish interest (just last week the local Jewish newspaper advertised for a trip to eastern Europe), by far the majority of such trips are to Israel.
But if you don't go for a visit you're not transgressing a commandment -- just missing an important connection to your land and people that you can't really experience any other way, and the opportunity to do a good thing and gain a place in Olam HaBa.1
1 I should note that Chazal list many things that either secure or preclude one's place in Olam HaBa and it is not clear to me how they interact. Untangling that is beyond the scope of this question.