Not really affiliated with the Edah, more Litvish, but quite chareidi: Marbeh Torah in Bnei Brak.
Not quite for absolute beginners, but relative beginners yes.
Also I know Belz have a yeshiva for BTs in Jerusalem.
Anyway, for current recommendations, you need to find someone in the know in Yerushalayim. Plenty of Americans in the Edah world there.