Definitely spend at least one night in Normandy proper (preferably 2–3). Otherwise you will spend most of your time simply getting there and back. Bayeux is an excellent base. Because you mention "tours," I am assuming your interest lies in the battle of Normandy in WWII. As far as tour versus no tour, it depends on your level of knowledge and your ability to get around. I have never taken a tour, but reports from those who have are every favorable. If you go sans tour, you absolutely must have a car. It is a large area and practically no public transportation.
Whether you take a tour or not, do everything you can to learn the history of this area before going (essential if you go on your own, but also very valuable if you take a tour). How much time, money and mental energy are you spending on your vacation? Invest just a few hours in a couple/few good books and movies to learn the basics of the lay of the land, the combatants, and their overall strategy and your investment will pay off in spades.