Question: When’s the best time to recite Kiddush Levana?
Answer: According to Rabbeinu Yona (Berachos 21a) one must wait two or three days after the molad, when the moon has begun to show a little light, before one can recite kiddush levana. While the Beis Yosef (OC 426) writes that for Kabbalistic reasons one should not recite kiddush levana until seven days have passed, the Mishna Berura (426:20; Shaar Hatziyun 426:18) writes that most acharonim disagree and hold that one may recite it after the third day.
The Shulchan Aruch (OC 426:2) follows the teaching of Maseches Sofrim (19:10) that one must only recite kiddush levana on motzaei Shabbos while one is still dressed in their Shabbos best. The Rema concurs, but adds that if one did not manage to recite kiddush levana on motzaei Shabbos, they should don their Shabbos clothes before reciting it during the week. Nonetheless, the Mishna Berura (ibid.) notes that many acharonim including the Vilna Gaon maintained that one should not push the mitzva off, especially in cloudy weather when it can be difficult to see the moon.
The Shulchan Aruch (OC 426:3) writes that one can recite kiddush levana up until the sixteenth day since the molad. He quotes the Maharil (19) who defines this time more accurately as half of a lunar cycle: fourteen days, eighteen hours, and twenty-two minutes.
While kiddush levana should not be recited on Shabbos or Yom Tov (Shavuos) for Kabbalistic reasons, the Mishna Berura (426:12) allows one to do so if it is the last possible opportunity.
In conclusion, one can begin to recite kiddush levana from the third day following the molad. One has up until the sixteenth day to say it. While it is preferable to say kiddush levana on motzaei Shabbos, one should not wait if one has an earlier opportunity. Ideally, one should not recite kiddush levana on Shabbos.