going to israel on vacation

Question

Why didn't the Lubavitcher Rebbe travel to Israel?

When someone asked him, he said that if he went to Israel, according to halacha, he couldn't come back to NYC.

So, is it forbiden to go on vacation in Israel and to come back to golus?

Answer 1

when someone asked him he said that if he go to israel according to halacha he couldn't come back to NYC so is it forbiden to go on vacation in israel and to come back to golus?

The Rebbe based this on a Rambam. The Rambam (Mishneh Torah, Laws of Kings 5:9) writes:

It is always prohibited to go from the land of Israel to outside of the land, except to study Torah or to marry a woman or to save (possessions) from non-Jews, and [then] to return to the land.

But this was not the main reason why the Rebbe never visited Eretz Yisrael. There are many encounters with the Rebbe, in which the exact same question is asked.

In 1991, a businessman called Yosef Yakir asked the Rebbe the question of why he never visited Eretz Yisrael. The Rebbe responded to him saying:

If you would write to me a halachic responsa that according to Jewish law, I would be permitted to afterward return to the United States, not to abandon the Jews here, then I would evaluate the validity of the argument to see if it is indeed a proper conclusion according to Jewish law. But to abandon all the Jews here, more than three million people! And it’s not just the American Jews. Some of the Russian Jews are settling here now in the United States, and when they come here, the ground must be prepared so they can continue in their Judaism. And this will be much more difficult to solve if I am in one place and they are in a different place.

The Rebbe felt great importance for the place where he lived and where he was able to help people. If he left that place, he would not be able to help people in growing in their Yiddishkeit.

A similair point was said by the Rebbe in 1973 to Moshe Ishon:

Any chassid who comes to ask about going to live in Israel, who isn't involved in education or in the rabbinate, is advised to go, and we give him our blessing for his move. The problem is for those who have vital roles in the community, and if they leave, everything will crumble. They are compared to ships captains in stormy seas; the captain is always the last to abandon ship. First, he must save the passengers.

There's a Hebrew letter, dating from 1983, titled: מדוע הרבי לא נסע לארץ ישראל - Why didn't the Rebbe visit Yisrael. In that letter, translated here, the Rebbe says:

I am using the expression “the front” advisedly. You surely know what is happening around you—the very same thing that is happening wherever Jews live, especially where they are a small minority—in terms of alienation from Yiddishkeit, loss of Jewish identity, intermarriage and outright assimilation. It is the duty of every Jew to do his or her very utmost to combat the forces that are threatening the very foundations of our people—first and foremost where he finds them in his immediate surroundings. (emphasis mine)

first and foremost where he finds them in his immediate surroundings - this is the main point.

With regard to your question whether going on vacation to Eretz Yisrael is halachically permitted, see this thorough answer.