I'm, specifically, interested in the state of nunneries during the reign of James VI and Mary I.
The nunneries of England and Wales suffered the same fate as the male houses, they were all dissolved 1536-40. The estates were either sold off or granted to favoured nobles or gentry, a few of the churches were preserved as parish churches (Romsey Abbey is a particularly fine surviving example) but most were converted into mansions by new secular owners or gradually demolished for building stone and other materials.
The dispossessed nuns got pensions, ranging from rather good to paltry, depending on how good they were at negotiating a deal when their institution was dissolved. We have a few cases of nuns continuing to live together after the dissolution, but most returned to their families. Some took secular employment and others married. Unlike the monks and canons, nuns couldn't get a job in the new Anglican church as it was boys only.
Mary I did have plans to refound a number of monasteries and nunneries but she only actually managed to do two before she died. One was Westminster Abbey, which was refounded as a Benedictine house for men (it was dissolved again at the beginning of the reign of Elizabeth I), the other was Syon Abbey in west London which was a Brigettine house which had both monks and nuns. Syon was dissolved by Elizabeth I but the community went abroad en masse and continued their religious life in exile. They lived in various places, finally settling in Portugal in 1594. The Syon nuns returned to England in 1861 and lived first in Dorset then Devon. The Syon community, the only English pre-Reformation religious house to survive with institutional continuity, finally died out in 2011 due to the old age of the last of the sisters.
The situation in Scotland was different. In 1560 the Scots Parliament abolished the religious function of monasteries and nunneries by banning Mass and other Catholic services which meant the round of 24/7 worship (the opus dei) that was a primary duty of monks and nuns could not continue. However, the former clergy were allowed to live in their old homes, supported by the income of the estates. Many chose to do so and remained in their abbeys until the end of their lives, though others went off and had new careers. As the the former monks and nuns died off from the 1570s to around 1600 the communities were thus extinguished. The property was either taken over by the Crown or granted to local aristocrats as secular lordships. There were quite a few former monasteries and nunneries that still had retired ex-clergy living in them in the reign of James VI.