Praying for the downfall of an antagonistic Sadducee: Berachot 7a
His notebook, on Mazalot and Days of the Week: Shabbat 156a
He would only travel to a mourner's home if he had died without children: Moed Katan 27b
Rushing to bring his son to school, while wearing a non-standard head-covering, in his haste: Kiddushin 30a
After a man was killed by a lion within three parasangs of R' Yehoshua ben Levi, Eliyahu the Prophet refused to appear to him for three days [R' Yehoshua should have prevented it]: Makkot 11a
Declaring regarding a law, "I heard it in this room!": Zevachim 13b
Family Interaction
Advice to his children: Berachot 8a
Teaching his children: Shabbat 68b
Telling his children not to prepare Matzah with Milk/Honey for the first night of Pesach: Pesachim 36a
R' Yehoshua used to say that he would not stand for his son, except that his son had married into the family of the leader of the Jews: Kiddushin 33b
Personal Practices
Cooling off on Yom Kippur and the 9th of Av: Yoma 78a Cursing those who sleep "Perakdan" [generally assumed to mean supine]: Berachot 13b; Niddah 14a
Wearing a Bamboo Shoe on Yom Kippur: Yoma 78b
Accepting a Levite's lineage based on testimony that he got the Second Ascension to the Torah: Ketuvot 25b
Accepted testimony of a man that his mother was captured but not slept with, when he spoke without awareness of the power of his words: Ketuvot 27b
R' Yehoshua ben Levi ruled that R' Shimon's opinion in a certain argument was reliable, in a case of pressing need: Gittin 18b-19a
Testifying as to the practice of the "Holy Congregation of Jerusalem": Rosh HaShanah 19b
After R' Chiyya bar Abba saw how R' Yehoshua ben Levi rushed to bring his son to school, he wouldn't eat breakfast before reviewing his son's learning with him and adding some new item: Kiddushin 30a
Citations
Set of quotations from the "people of Jerusalem": Pesachim 113a
Set of statements on the giving of the Torah: Shabbat 88b-89a
Set of declarations on the status of certain cities as walled or non-walled: Megillah 3b-4a
Two statements on the value of Torah study: Makkot 10a
How he began his discussion of the Purim Story: Megillah 10b
Citing a legal statement which R' Yehoshua ben Levi made without explanation, and commenting, "This is prophecy!" [Rashi - And R' Yehoshua ben Levi wouldn't have said it without a tradition from his elders]: Eruvin 60b
R' Yehoshua ben Levi mentioned there were 24 instances of a certain law, and when R' Elazar asked that he enumerate them, R' Yehoshua ben Levi said, "Go find them": Berachot 19a
Rabbah bar bar Chana reported a lesson in the name of Rabbi Yehoshua ben Levi, to which Rav Chisda replied, "By Gd! Even if Rabbi Yehoshua ben Levi himself would say this, I would not listen to him!": Berachot 24b