Normandy is where several of the stories people carry around about Western Europe happened within a few hours' drive of each other. Vikings settled the lower Seine valley and the region takes its name from them. In Rouen in 1431, Joan of Arc was burned at the stake. In 1066 Duke William of Normandy won the Battle of Hastings, and the Bayeux Tapestry tells how. And on 6 June 1944 the Allies landed on beaches that are still here, with the bunkers and the cemeteries to go with them.
This is a region guide, not a city guide, and it plans around two places to stay: Rouen for the first night, then Bayeux for the next three, with a long last day at Mont-Saint-Michel. Be honest with yourself about transport before you book. Rouen and Bayeux are easy on foot and by train. Étretat, Honfleur, the D-Day coast and the Mont are spread out, buses are thin, and a car (or a guided minibus from Bayeux) is the realistic way to do them. And you can't see the Bayeux Tapestry right now: its museum is closed for renovation and the embroidery is on loan in London, so Bayeux here is built around the cathedral, the war museum and the coast.
Day one is Rouen: the cathedral, the Joan of Arc sites and the Gros-Horloge. Day two is the long drive, past the cliffs of Étretat and the harbor of Honfleur to Bayeux. Day three is Bayeux and the British and Canadian beaches, day four the American ones around Omaha, and day five Mont-Saint-Michel. Most people arrive through Paris, which has its own plan in 5 days in Paris, and Normandy is one of the easiest parts of France to add to it. Start on a Wednesday: the Joan of Arc museum and the Gros-Horloge are closed on Mondays, Rouen's fine arts museum on Tuesdays, and a Sunday at Mont-Saint-Michel works well.