Another vote against the Caen "museum." I really feel that if Rick didn't fawn over it, few Americans would make the trek. There are much, much better museums in the D-day area, including my favorite, the Utah Beach Landing Museum. Fortunately, another great museum is right in Bayeux. The Museum of the Battle of Normandy gives a good general overview of the battle—much better than the Caen place IMHO. As mentioned, the D-day Museum in Arromanches is also well done (although I'll admit I haven't been since they redid it a couple of years ago). It isn't as comprehensive, but it concentrates on the artificial harbors that were used to resupply men and matérial in the weeks after D-day—the remains of which can be seen onshore right outside of the museum. Also the Overlord Museum (outside of the Normandy American Cemetery) and the D-day Experience (Carentan) are worth visiting.
Get a car!!! Normandy is not well served by any sort of public transportation, and it is a long way between sites (45 miles between the five beaches as the crow flies, and you won't fly). But driving in France and particularly Normandy is easy. Just learn about and watch for the speed limit signs (some don't say the speed, they simply say things like "leaving the village," which means the speed limit reverts to its previous state). There is also a speed radar site right on the N13 between Bayeux and Sainte-Mère-Église heading East by the town of Isigny-sur-Mer. There is no tolerance for even a kilometer over the speed limit in France (i.e., no "grace" limit like in much of the U.S.). And you won't even know you got a ticket until it arrives in the mail long after your trip with an additional charge from the rental car company for the courtesy of sending it to you. That being said, GET A CAR. I can't imagine visiting Normandy without one, and there is so much to see when you get out of the town centers, including areas of action, and several well preserved German artillery compounds.
Bon voyage!