Most Jews of the Diaspora are usually offered a sponsored trip to the homeland when we reach the age of 17. These are known as heritage or birthright trips, and they are usually made between the ages of 17-26 (though some of us go later). Many Jews have been, as I have, but some have not been able due to various circumstances.
But you don't have to go to Jerusalem to get accurate information. It's all there in encyclopedias, the Internet, or just ask a Jew. There are many Jewish websites to learn from too, such as MyJewishLearning.com where anyone can get an overview of the various facets of Judaism, it's practices, and its history.
Jerusalem was never completely destroyed either by the Babylonians or the Romans. Even the secular historical accounts are a bit exaggerated. For instance Josephus writes that more than 1.1 million people died in the Roman siege and almost 100,000 were led away as captives, leaving Jerusalem itself as a desert. The truth is that there were only about 1 million people living in the area to begin with, and there were still enough Jews living in the area from which the Bar Kokhba revolt would rise some 50 years later.
The dates of 587 B.C.E. and of 70 C.E. are the dates of the Temples falling and the seiges, but in both cases people were still left living in Jerusalem after the Temples came down.
We annually observe the Temple losses on a holy day of mourning we call Tisha B'Av, the 9th day of Av. Both Temples according to tradition fell on the same day, and oddly enough the Alhambra Decree of 1492 that expelled the Jews from Spain also went into effect on Tisha B'Av (though it was actually promulgated on the 7th of Av). So we yearly keep in mind what happened on these dates by particular customs.
But the cities that stood then were not totally destroyed, per se. As I mentioned above, there is an obsession with these dates by the JWs and some Christians who teach that this is what happened. Especially the 70 C.E. siege of Jerusalem gets imagined as if all Jews were taken away and as if Josephus' account is Christian gospel. Historians know it isn't, and they strongly doubt that the Christians went to Pella as the Jerusalem Church was left intact until the Bar Kokhba revolt in 135. I am supposed to be of the tribe of Judah and House of David, and the last bishop, Kyriakos, is supposed to be a relative to my ancestral line (most of my family was already in Seferad/Spain by this time).
Because I had relatives who were among then first Hebrew Christians, and they were living in Jerusalem when the Bar Kokhba revolt began, many scholars doubt the Pella story (or that it was as significant or supernatural as legend made it into). Judas Kyriakos was believed to have perished during the revolt in Jerusalem in 135, so what would the bishop of Jerusalem be doing in Jerusalem if there was no Jerusalem then and all the Christians had gone to Pella 50 years before? The Temple itself was completely plowed down and covered only after the Bar Kokhba revolt.
Also, after the Bar Kokhba revolt ended, the Romans would allow Jews to enter once a year on Tisha B'Av. The city itself was not totally demolished even then. Only the Jews were barred from living there.
The idea that Jerusalem was leveled was a convenient invention that supported the Christian view that God had totally rejected the Jews and punished them for their act of deicide. In fact, it would not be until the last quarter of the 20th century that the Roman Catholic Church would officially change its view on matters, reject the idea of the Jews being abandoned by God, and lift all charges of deicide. Since then mainstream Christianity has also abandoned the idea of a "totally demolished" and thus "rejected" Jerusalem.
These dates the Watchtower holds to mark only Tisha B'Av, the loss of the Temples, and not the destruction of the city of Jerusalem.