Rouen or Chartres?

In your case, Rouen is more convenient (saves 1 hour of driving), and I cannot say if the cathedral there is "better" or "worse" than Chartres' as they're both magnificent!
Don't "just" see the cathedral: pop by St Maclou church as well, and walk down rue du Gros Horloge.
There is a paid parking garage right at the cathedral, called, well, Parking de la Cathédrale: head there to park.

Hands down, Chartres! Probably the most magnificent Gothic cathedral in the world. Try to schedule a private tour with Malcolm Miller who has made Chartres his lifetime passion. He truly knows how to bring the art and architecture to life. He’s getting up there in age, so hopefully you’ll be able to book him. He has trained his successor, Ann Wood?, who now gives the public tours. I would definitely book a tour, if you can. I had my very first visit to Chartres with Malcolm Miller back in the 80s, and it left such an impression on me because it was the first time I got a glimpse into the world of Gothic cathedrals. I think it was probably why I went on to study European history in college. I’ve since been back twice, having another Malcolm tour each time. Rouen is beautiful, and your time there would be well-spent. However, Chartres will stay with you for a lifetime.

The cathedral in Bayeux does not at all rank in terms of "great cathedrals" (though it is still lovely and impressive) so scratch that off your list. Obviously Rouen is a shorter drive on your fastest route and makes more sense logistically but if you don't mind the extra hour or so of drive time on your way from Ver-sur-Mer to Versailles then I agree with Beth that hands down the answer is Chartres as it is probably the greatest and most iconic of gothic cathedrals. And unlike the cathedral in Rouen it never suffered bombing damage during WWII. The majority of the stained glass windows and sculpture/statuary is original from medieval times. The medieval stained glass windows alone make the cathedral worth a visit. All the info you need to plan your visit can be found on the Chartres tourist office website (the medieval town center is also lovely and worthy of exploration):

https://www.chartres-tourisme.com/en/do-not-miss/the-chartres-cathedral/visiting-the-cathedral#

And speaking of bombing damage during WWII there is a great story about one individual American soldier who saved Chartres cathedral from being bombed and destroyed during WWII. The allies were closing in on Chartres and feared there may have been snipers in the cathedral spire. Not wanting to risk the lives of soldiers an order was given to blow up the cathedral. But one American soldier, named Welborn Griffith, stepped up and requested that he be allowed to do recon and climb the spire to verify the presence, or not, of Germans in the cathedral spire. With one other private he snuck into town and climbed the spire and confirmed there were no Germans present in the spire and the order to blow up the cathedral was withdrawn. This guy was a real bad ass (and hero) because later the same day he was advancing with a troop of tanks and as the tanks came under fire he jumped onto the front of one of the tanks with his machine gun to return fire. He was unfortunately killed during his valiant attempt.

The townspeople somehow managed to understand who this soldier was and how he saved their cathedral but when they saw his dog tags they got his name wrong (the last name comes first on dog tags) and thought he was named Griffith Welborn. They erected a memorial to him on the spot where he fell but due to the mix up in his name his family and no one else knew of what he had done. A local historian performing research in the 90's uncovered the mix up and attempted to track down his surviving family members in the U.S. They found his daughter and let her know of what her father had done and invited her to the cathedral where a full military band service was performed inside the cathedral and the memorial was rededicated to reflect his proper name, Welborn Griffith. He fell in the town of Lèves, just north of Chartres, and each year on August 16th (the date he was killed) there are flowers placed in front of the building where he died in action.

Mystique, what a fascinating story! Thank you for sharing it. And, I agree with you about the Bayeux cathedral. Lovely, but nowhere near the preeminence of Chartres. I do, however, find the town charming…and don’t get me started on how spectacular I think the Bayeux Tapestry is. But, that’s a whole other topic for another post. 🙃

Thanks Beth. I'm a history nerd and I'm especially interested in French history. Much like a Jeopardy contestant, I have a head full of useless, trivial knowledge. ;)

Chartres Absolutely. Is Malcolm Miller still giving his lectures on the stained glass. I feel so lucky to have experienced that and last I heard he was still doing it occasionally. If so it is worth arranging that.

Rouen is also great but Chartres is the best. Bayeux is a quite ordinary church much like dozens all over France. Yes worth the visit, but not in the class of Rouen or Chartres.

Janet - If you click on the link I provided you'll see that Anne Marie Wood is now doing the public tours but both she and Malcolm are available for private tours as well. If anyone has the budget for a private tour then I'd take advantage of doing the private tour with Malcolm, who is considered the pre-eminent expert on the cathedral, though I'm sure he would not have handed this job off to Anne Marie if he felt she wasn't up to the task as the cathedral in Chartres is something he has devoted his entire life to. I remember on another travel forum a few years ago where someone asked if Malcolm was still alive and he responded personally to say "I'm not dead yet and I'm still doing tours!" If in early 2024 he is "still alive" then for a Christmas gift I plan on asking my French in-law parents if they will buy me a gift certificate to do a private tour with Malcolm for me and my wife. That would definitely be a "bucket list" experience for me but hopefully "kicking the bucket" will not be something Malcolm has done prior to that time.

In the cathedral book shop you can buy the book that Malcolm wrote about the cathedral and use it as a guide as you walk through the cathedral and it explains each window and piece of statuary that you'll see as you are walking around the cathedral, both inside and out.