I did a Normandy road trip with a friend way back in 1990. We did just 4 nights, a different stop every night, and I'm amazed looking back at how much and how much ground we covered in that short time. But distances are short, so with a car we were easily able to drive from town to town, stop, explore for an hour or two, and move on.
Here's what we did. It was at the tail end of a tour of England. We took a train from London to Portsmouth and a ferry to Ouistreham, then a bus to Caen where we spent the first night.
Next day we picked up our rental car and drove to Bayeux, where we spent a few hours to see the tapestry and the cathedral. I wish we had spent more time there. We drove to Coutances (beautiful cathedral) and then Granville (charming town with an old town at the top of cliffs with great views), and then to Dol de Bretagne, where we spent the night.
Next day we went to Mont-Saint-Michel, and we spent the night there, which was worth doing, as the crowds were massive during the day (even almost 30 years ago).
Next day we headed east. I don't remember all the stops we made along the way, other than Falaise, which was worth a short stop. We spent the night in Lisieux, which was the only really bad choice we made. It has a basilica devoted to Saint Teresa, and the entire town seems to worship her (including all the souvenir shops). Being non-religious people, it was not the best choice for us to spend the night.
Last day we drove to Rouen. We also stopped at Jumieges Abbey, which I absolutely loved and highly recommend. We also made a short stop in Tancarville, and while I don't remember much, from my pictures I can say it was well worth visiting if only to see the chateau. Next we went to Honfleur, which is so delightful -- another highly recommended stop. After all that we got back to Ouistreham, dropped off the car, and caught an overnight ferry back to Portsmouth so we could catch our flight home from Heathrow the next day.
So to summarize, so many wonderful places to see in Normandy, but many of them are small towns and villages that you can enjoy in a short visit. Distances are short and the highways are two-lane roads through rural rolling hills. In May 1990 there was little traffic. I don't know what it would be like now. I highly recommend the stops I've boldfaced above. You can do it in more time and I'm sure if you do, you will discover many more delights than we did.