Why did Reb Yochnan only ask Yavneh and it's wise men instead he should of asked for all of Yerushlayim (which Medrash Eicha says he did) to be saved?
תן לי יבנה וחכמיה ושושילתא דרבן גמליאל ואסוותא דמסיין ליה לרבי צדוק קרי עליה רב יוסף ואיתימא רבי עקיבא (ישעיהו מד) משיב חכמים אחור ודעתם יסכל איבעי למימר ליה לשבקינהו הדא זימנא והוא סבר דלמא כולי האי לא עביד והצלה פורתא נמי לא הוי
Looking back fifty years later, Rabbi Akiva remarks that G-d must have clouded R' Yochanan ben Zakai's judgment, as indeed, why didn't he ask for Jerusalem?! The Talmud then observes that R' Yochanan's thought process was very straightforward: ever the pragmatist (he'd retired from business at age forty), R' Yochanan feared that if he asked for Jerusalem, he'd be shown the door before getting the chance to bargain for anything else. He chose the lesser of evils, accepting the loss of Jerusalem and planning for a Jewish future without it.
I heard in a Shiur that Reb Eliyashiv answered In our Gemara he also asked for Yerushlayim to be saved. He asked for Reb Tzadok to be saved, the reason Rav Tzadok was sickly was because he was Fasting trying to prevent Yerushlayim from being destroyed. He was saying if you end the siege of Yerushalyim, that would be a doctor enough and Reb Tzadok will be saved.It was a diplomatic request to end the siege on Yerushlayim.