After the obligatory prayers, Tahajjud is the best prayer to come closer to Allah and, thereby, improve our spiritual health. And the best time to pray Tahajjud is at the last part of the night. The blessings of this prayer is pretty self explanatory from these 2 hadiths:--
"The closest that a servant comes to his Lord is during the middle of the
latter portion of the night. If you can be among those who remember
Allah, the Exalted One, at that time, then do so." (Tirmidhi).
"Observe the night prayer; it was the practice of the righteous before you,
and it brings you closer to your Lord, and it is penance for evil deeds and
erases the sins and repels disease from the body." (Tirmidhi).