Henry came to the throne in a kingdom that was in anarchy after King Stephen's reign. He got the Barons into line with remarkable speed. The bulk of his lands were however in France, having acquired Normandy and Anjou through inheritance and much of south-west France through marriage to Eleanor of Aquitaine. It was because of these land holding that the English Kings claimed the throne of France until the 15th Century.
Henry II received a lot of bad press due to the murder of Thomas Beckett, but it was all a misunderstanding. Honest.
Henry's family was beyond dysfunctional. Eleanor spent most of her married life in prison and his sons were regularly at odds with him. Richard even attacked Henry with the aid of Louis VII of France. Still, Henry managed to outlive two of his sons. Henry's legacy was squandered though when Richard lost his money crusading and getting captured, while John Lackland justified his father's lack of faith in him by losing his French posessions as well as the respect of the Barons.