Quality of life is somewhat subjective -- do you prefer wine or beer? Does Italy's sunny Mediterranean climate appeal, or is it too hot and you'd prefer the cool dampness of England? -- but in terms of standard of living, I would say Northern Italy and the Low Countries had the highest standard of living in the high to late Middle Ages. (Described in the Cambridge Economic History of Europe (Rich and Wilson) as a quadrilateral between Florence, Genoa, Milan, and Venice and a strip from Ypres to Antwerp, respectively.)

Early in the Middle Ages, it's a little harder to say. Civilized areas like Umayyad Al-Andalus and the Byzantine Empire likely had the most sophisticated economies, but some archaeological evidence suggests that perhaps Western Europe in the Dark Ages (e.g., Carolingian France) was a fairly good time to be an average peasant, in comparison with both the average peasants of more civilized areas and in comparison with the average peasants of the later Middle Ages (e.g., Valois France), at least in terms of material wealth and health, if not in terms of security (i.e., chance of being killed/raped/whatever by Magyars, Vikings, or local noble thugs).