Chartres, Versailles or Reims?

I would suggest Versailles and Chartres, in no particular order. Versailles is of course an incredible sight, but it is accordingly more crowded and requires some advance planning for tickets (in "normal" times at least). Chartres has a stunning cathedral, relatively few crowds in my experiences, and a beautiful old town that is architecturally very different from what you can see in Paris.
Both destinations are easy to reach by train: regional trains leave from Montparnasse station every 30-60 minutes for Chartres, and for Versailles there are several routes by suburban train.

As for Reims: the train is more expensive and requires advance booking, I prefer the cathedral in Chartres (better preserved), and I do not find that there is that much to see in town otherwise. Granted, I have zero interest in champagne.

I agree that Versailles and Chartres are the must sees. Especially since they are easily accessed from Paris as day trips. Tours are available for both, but you do have public transportation available. I have been to both twice and would gladly go again. They are both vivid memories for me.

I have never been to Chartres. Versailles is an option, but the least of my favorites. I would suggest another option. You might want to consider taking a guided tour of some chateaus in the Loire Valley. The city of Tours has guided tours originating from there. I did an all day tour with Bordovino. It was excellent. They usually meet right near the train station in Tours.

https://www.alafrancaise.fr/loire/139-chambord-chenonceau

I think the Loire is too far and spread out for a day trip from Paris, though I'm sure there are good tours. My vote would be for Chartres or Versailles, depending on whether you like cathedrals or palaces better. Reims' beautiful and historic cathedral was bombed in WWI and went through major restoration. It looks great and I think the restoration was careful and true to the original design (others may correct me). Chartres has looked the same for 600+ years. Recently the stained glass windows were cleaned so the light inside must be much better. If the legendary Malcolm Miller is still giving tours that would be a bonus.

But with only 2-3 full days for Paris itself, do you really want to spend one of them elsewhere? Maybe this isn't your first time.

I would recommend Chartres (not only because I used to live there, but it's an amazing city). You can also visit the Château de Maintenon from Chartres very easily via train.

The crown jewel of Chartres is no doubt the cathedral. If you can score a tour from Malcom Miller - vas-y. There is a lovely Musée des Beaux-Arts in town and also a stained glass museum. Plus there is no shortage of delicious restaurants. The centre ville is lovely, especially down by the river.

The train to the City of Tours is only about 1:15. I would agree, you have to take a tour because the local travel on your own in the area would be lengthy. However, it is very doable for a day trip and a different experience than the other 3 mentioned day trip places.

I would definitely visit Versailles. It's only a short train ride from central Paris and definitely great to experience. The cathedral in Chartres is beautiful and the town is worthy of exploration. I haven't been to Reims other than driving by on the A4. So after Versailles I'd go to Reims (and Epernay) for champagne.

Versailles is hard to compare with Chartres and Reims, but it would be my choice as it is so unique and so incredibely over the top, you have to see it. Even with the crowds and the long lines at the entrance. Chartres as a whole is more charming and in this respect to prefer above Reims, but it depends about further interests what will be your preference. If you want to enjoy a gothic building with stained glass there is always Sainte-Chapelle to visit not so far from Notre-Dame in Paris.

As Alexander already remarks you can combine Chartres with Château de Maintenon, the garden in June is in full blossom, with sunny weather very enjoyable.