Where did friars live?

Catholic Answer

A friar typically lives in a Friary, this applies to Franciscans, Dominicans, Carmelites, Augustinians, and Servites. Monasteries are were the monastic orders reside: Benedictines, and Cistericans.

Follow-up answer: The question is posed as if Friars are a thing of the past... like Friar Tuck in the story of Robin Hood. Friars are alive and well throughout the world. They differ from monks in that monks tend to be cloistered in a monastery, serving the world through prayer. Friars, on the other hand, live in Friaries, and serve the world by working out in it... serving the poor, working in hospitals, soup kitchens, homeless shelters, nursing homes, and a wide variety of other pursuits.

Monks usually commit to one community location... one monatstery, for life; and end-up buried, after death, in the monastery's cemetery, out back. Friars, on the other hand, commit to community, but most Friar communities have multiple locations; and so a Friar may live in one Friary for a while, then move to another within the same community, and so on. Friars, too, end-up, after death, buried in the community cemetery, which may be centralized at just one of the community locations, or each location may have its own cemetery... it all just depends on the community.

Depending on the community, it's also possible for Friars to live separate from their communities, when on some kind of special assignment; or if they're not avowed and maintain secular jobs. Again, it depends on the community, and its rules.
They live in a friary, a monastery, a church rectory, or another type of church residence.