Are there better things for a Jew to do than sleep?

(4) Such is the way of Torah: eat bread with salt, and drink small amounts of water; and sleep on the ground, live a life of privation, and toil in Torah. If you do this, “Happy shall you be and it shall be good for you” (Psalms 128:2): “Happy shall you be” in this world, “and it shall be good for you” in the world to come.

Another thing. God said to Moses: “It was good for me that I was humbled, so that I might learn Your laws.” (Psalms 119:71). It was to Moses credit that he was given 120 days [on Mount Sinai] when he received the Torah.

....How do we know that he did not sleep nor doze? It is like a king who loved his servant. He said to him: measure out for yourself golden dinars. He was so overjoyed he did not need to eat or drink. He needed sleep. He said: If I sleep I will forgo these!

So did Moses measure out Torah. He forgot and neither ate nor drank. He needed to sleep. He said: If I snooze I will lose! For did He not say just 40 days?

Said the Holy One: You suffered but you will not lose out! On the first tablets, only the Ten Commandments were written, now that you have suffered, I will give you halachot, midrashim, and aggadot.”

“Of David…Keep my soul, for I am pious” (Psalms 86:1–2). Levi and Rabbi Yitzḥak. One said: so said David before the Holy One, Blessed be He: Master of the Universe, am I not pious? As all of the kings of the East and the West sleep until the third hour but “At midnight I rise to give thanks” (Psalms 119:62).

(2) ....Our masters said: For the twelve months that Noah spent in the ark, he did not taste a bit of sleep neither by day or night because he was busy sustaining the souls who were with him. Thus it says “a wise one wins souls.” (Prov. 11:30) This is Noah.

(4) Rabbi Chananya ben Chakhinai says: One who stays awake at night, and one who wanders on a road alone, and one who turns his heart to idleness, such a one is liable for [forfeiture of] his life.

MISHNA: One who says: Sleeping is forbidden for me..... if he violates the vow he is guilty of “He shall not profane his word” (Numbers 30:3).

But didn’t Rabbi Yoḥanan say that the one who takes on oath “that I will not sleep for three days” the court flogs him and he may sleep immediately.

MISHNA: [...] On Yom Kippur eve at nightfall, they would not allow him to eat a great deal because food induces sleep

MISHNA: If the High Priest got sleepy the young priests would snap their fingers before him, and say to him: My Master, High Priest. Get up and chill yourself once on the floor. And they would engage him until it was time to do the sacrifice.

GEMARA: [...] the prominent men of Jerusalem would not sleep the entire night so that the High Priest would hear the noise in the city and not be overcome by sleep.

A baraita of Abba Shaul: They did this even further out in memory of the Temple. But they would sin! Abaye said - and some say it was Rav Nahman bar Yitzhak who said - : That refers to Nehardea, as Elijah the Prophet said to Rav Yehuda, brother of Rav Salla Hasida: You ask why has the Messiah not come? Isn’t today Yom Kippur, and relations were had with several virgins in Nehardea?

(4) Even though we blow the shofar on Rosh Hashanah is a Scriptural commandment, it hints at saying: “Wake up sleepers from you sleep, and slumberers from your deep sleep! Examine your conduct, do repentance, and remember your Creater!

...And so it became a universal custom to rise early during those ten days, to say prayers of supplication and ardour till the dawn of the day.

There are also those who do not sleep during Rosh Hashana during the day (according to the Jerusalem Talmud) and this is the correct thing to do.

A braita: Rabbi Yehoshua ben Hananya said: When we held the water drawing celebration we did not see sleep in our eyes the entire Festival.....

Really? But didn’t Rabbi Yoḥanan say that the one who takes on oath “that I will not sleep for three days” the court flogs him and he may sleep immediately. Rather, this is what Rabbi Yehoshua is saying: We did not experience the sense of actual sleep, [but] we dozed on each other’s shoulders.

MISHNA: If some [participants at the seder] fell asleep, they may eat [from the Paschal lamb.] If they all fall asleep they may not eat any more. Rabbi Yosei says: If they dozed they may eat, but if they fell asleep they may not eat. The Paschal lamb after midnight make the hands ritually impure, piggul and notar make the hands ritually impure.

(7) Rabbi Chanina said: In the third month the day is double the night, and the Israelites slept until two hours of the day, for sleep on the day of Azereth is pleasant, the night being short. And Moses went out and came to the camp of the Israelites, and he woke the Israelites from their sleep, saying to them: Arise from your sleep, for your God desires to give the Torah to you! The bridegroom is ready to lead the bride and to enter the bridal chamber. The hour has come for giving you the Torah.

...if he is accustomed to take an afternoon nap he should not forgo it for it is Shabbat joy for him. And after he sleeps he should study Torah.

Sleep on Shabbat is a pleasure. So long as he does not have too much sleep such that it leads him to wasting [time that could be used for] Torah. For Shabbat was only created for studying Torah....

For it says in the midrash: said the Torah to the Holy One, “Lord of the Universe, when Israel enters the Land, this one will run to his orchard, and that one will run to his field and what will happen to me?” Said the Holy One “I have a partner who I will match you with. Her name is Shabbat. For they are free from their work on Shabbat and will be able to attend to you.”