The Buddha didn't find monastery, but when he start to sharing his teaching with people, they offered some places for the Buddha and his Disciple. Furthermore, he made a rule for monks and nuns which in raining season(3 month), they should be stay one place without wondering as usual.  

(Mv I 13: Bimbisārasamāgamakathā — The Discussion of the Meeting with (King) Bimbisāra: The King of Magadha, followed by 120.000 householder an Brahmans, approached the Buddha and received the Dhamma. The King Bimbisāra of Magadha offered the first monastery for the Saṅgha and the Buddha allowed his Bhikkhus accepting monasteries.)