According to Wikipedia's Buddhist monasticism article, the Buddha formed the first monastery. There is no source, 'though. To quote:
Buddhist Monasticism is one of the earliest surviving forms of organized monasticism in the history of religion.
The order of Buddhist monks and nuns was founded by Gautama Buddha during his lifetime over 2500 years ago.
Ok, so it doesn't specifically say 'monastery' here but still, an order of monks and nuns, some sort of precursor to a monastery at least.
According to History World's History of Monasticism:
Leading his followers into holiness a generation after Mahavira, Buddha also organizes them into communities.
Is this just "according to tradition" or is there historical evidence of him forming a monastery/order/community: such as archaeological findings or non-religious texts? If yes, is there's anything left of the original or has it all branched out?