What would a Knight do when not at war, and what exactly was a fief that a knight ruled over or owned? I guess this question would be directed towards English or French knights, since I guess there would be more info about them, but I'd love to hear about other knights if you have knowledge about them.
First, let's define the fief. This is a grant of land, of variable size, given to a lord or knight in exchange for military service to a higher lord or king. The base unit of exchange would be the manor, which could vary in size, but frequently consisted of a village (50-300 people, perhaps) and the surrounding fields, pastures, and woodland. That, at least, is the theory; in reality it could be considerably more complex.
The leisure activities of a knight or any other member of the military aristocracy largely revolved around training for war. Hunting was immensely popular, but so were tournaments, which became hugely popular in the early 12th century.
Let's look at William Marshal as an example of the High Medieval knight. He lived during the late 12th and early 13th century, and was a younger son of a minor Anglo-Norman baron (landowner subordinate only to the king). He was born in England, but resided in France from age 11 to 20, and later spent time both in England and in France. Prior to acquiring land, he was a member of the households of powerful lords, such as William de Tancarville and, later, Prince Henry of England. During this period, he became perhaps the most renowned tournament fighter in Europe. These were not the civilized jousts of the later Middle Ages, but mock cavalry battles, and were the all the rage among Europe's young noblemen. Marshal fought in dozens or perhaps hundreds of these very rough, dangerous tournaments, and the fame he gained in them helped him to acquire lands and rise to a very high station, ending his life as Earl of Pembroke.
Crouch, David. William Marshal: Knighthood, War, and Chivalry.