Someone recently wrote a sweet little meditation on the 'cloister' as the heart of the monastery.
People have romantic notions of monastic life - which may explain why many come away from it sad. Some monks and nuns have no physical cloister in the classic sense. Some houses do not have a structural quadrangle around which the physical cloister is formed. Cloister is a term for enclosure used by enclosed religious, monks and nuns. Some communities have strict Papal enclosure. It's technically about separation from the world. There used to be semi-cloistered religious who maintained enclosure with a separate convent or house, including refectory and living quarters - often attached to the facility in which they worked. They still exist of course in orders such as the Little Sisters of the Poor, or active Dominican congregations, as well as friaries and priories. Again, it's a practical matter, as well as a canon law requirement I think, and it's about separation from the world.
The lovely architectural enclosure found in traditional monasteries and great abbeys is only part of the cloister - but it is not the heart of a monastery. The heart of the monastery is the Opus Dei, the work of God - hence the location of the heart of the monastery would most likely be the choir, the monastery chapel or church.
Unless the monks make ale - then it could be the brewery for some.
When I was in the monastery there was a funny novice who liked to go to the quadrangle, his hood up, arms beneath his scapular, pacing meditatively. None of the monks used the quadrangle except to tend the garden. The cell was the normal place for meditation and prayer. Some of the brothers would snicker about our little brother playing monk. He had very romantic notions of monastic life, and he soon left, rather disappointed. Monastic life is completely ordinary - no drama - ever.