Why did Hashem bury Moshe in an unknown place, and did not do so with other great Tzadikim like Avraham, Yitchak and Yaakov?
Moshe had a very different role in all sorts of ways.
One answer might be, based on the Meshech Chochmah, that Moshe had a higher level of prophecy than anyone else, but because of that, there was the problem that people might think he was a god too. Also, he was such a great leader that the people felt they couldn't manage without him (that's why they built the Golden Calf).
If everyone could visit the "Moshe Rabeinu Grave Site", first of all, some people might try to worship him, and more importantly, the Jews might have refused to leave there. So this way, Hashem said: "I'm burying Moshe, I'm not telling you where; the point is he's dead now; you'll cry for a few days, but then you'll have to get up, move on, and follow Yehoshua into the land of Israel."
Rabbi Wein always quotes the maxim: "No man is indispensable, yet no man is replaceable." This is very true. No man is indispensable to the extent that "we cannot continue onward." Yet no man is replaceable either. People have their own unique contributions that can never be replaced.
This is another explanation of why Moshe's burial place is not known. The Jewish people had to move forward. They had to continue with the next leader and the next generation. "A generation passes on and a new generation comes." [Koheles 1:4] We can only go to the leader who is present in our own generation. This is the way of the Torah and this is the way of the world.way of the world.
Avraham, Yitzḥak and Ya'akov were not national figures at the time that they lived. They were fathers, and even leaders of their small clans and growing tribes. But they never led a nation the way Moshe ultimately did. Moshe had led the nation to hear the word of G-d themselves, and when they were not capable of withstanding that experience he acted as intermediary and delivered the word of G-d to them. He was also a national leader who had led them out of Egypt and led them for 40 years as the equivalent of a king, providing for them (with the aid of G-d) when they were hungry and thirsty and leading them to success in battle. Despite the occasional mishap he was much beloved as well. Even aside from the level of prophecy Moshe attained, it is easy to understand why the people might have refused to go on without him and might have even begun to worship him had his burial place been made known.
According the the BaH on Sotah 14a, Rabbi Hama son of Hanina says that Moses' burial site was hidden because God knew he would eventually destroy the temple and exile Israel from the land. If they knew where Moses' burial site was, they would go to it, alert Moses of the evil decree, ask him to pray for us, and Moses would nullify it.
He proves that Moses was unique in his decree-nullifying ability, citing the sin of the golden calf, and pointing out that of all the righteous people in the generation, Moses alone was approached by God to intervene.
He also remarks that the righteous are even more precious in death than in life, which would exacerbate Moses' special role.
To answer the second half of the question: and did not do so with other great Tzadikim like Avraham, Yitchak and Yaakov?
Moshe was not allowed to enter Israel. Perhaps this rule was also true after his death, and not just before it. All the other great tzadikim were burried in Israel. (Except for Aaron and the generation that died in the desert... but that's a separate question.)
Another reason Moshe's burial is unkown, in a kabalistic sense, and I wont quote a source: Moshe did not need to be buried. He had perfected his body in a spiritual sense so he did not need to decompose and regenerate. This is alluded to where there is no vertical line between "Moshe Moshe" in the Torah, as there is for "Avraham | Avraham".
No sources. If you dont like it - move on. The answers above are good.