Day Trips from Colmar

Beaune is quite far from Colmar. I do not believe the train will take you there from Colmar. France train travel is like spokes coming out of Paris. I think you'd have to take a train back to Paris and then back out to Beaune. Beaune is nice, but we used a car to go from Alsace to Beaune/Burgundy. I liked Ribeville and Haut Konigsburg (medieval castle). Kayersberg, was nice, home of Albert Schweitzer.

A train will not get you around the sights in Alsace. There is a north-south line linking the big towns (Strasbourg - Sélestat - Colmar - Mulhouse). With links in all directions from Strasbourg and Mulhouse. The places you want to go are small villages mostly in the vineyard areas, along the foothills west of the towns.
Lots of info in this official website: https://www.alsace-wine-route.com/
To get to these places you need an (infrequent) local bus, or better still a car. You can then visit two or three villages in a day (Ribeauvillé, Riquewihr, Kaysersberg, Eguisheim and many more). Don't miss Haut-Kœnigsbourg castle.

If you like medieval, with a car you can also visit Freiburg im Breisgau, on the other side of the Rhine. Use the "Park and Ride".

You can also reach Basel by train, that scores high in the medieval eye-candy rating. See photos here: http://www.armandobraswell.com/wp-content/uploads/2015/06/munsterplatz_compressed.jpg
and here: https://www.danimu.ch/basel3/

There are TGV (High Speed trains) from both Mulhouse and Strasbourg to Paris. And local trains will allow you a day trip to Strasbourg.

As the others say, Beaune is not in Alsace, it is in Burgundy, half way across France.

I spent several days (with a car) in Eguisheim. It was an excellent base, very small so no traffic and a short drive to the main road, but honestly not much to see. The other villages were much more interesting. There's a ruined castle, Château du Haut-Kœnigsbourg that's well worth visiting. I don't know how you'd get there, but very close by is Monkey Mountain, where you get to interact with a large colony of Barbary apes (cute small monkeys).

I'll just add, that my trip to Alsace was my 2nd trip to Europe, first to France and first time renting a car in Europe. I'm not sure your rationale for train/rental car, but I'll say that Alsace was quite an easy place to drive. What we did was to take a train from Paris to Colmar, picked up a car for Alsace, then drove to Burgundy and then Loire, returned the car and took the train back to Paris. In general, I prefer train travel, but for some locations, it just doesn't work. Also, I'm just picking up that you are traveling in January. I would double check that places are open and the the weather will be what you'd like for your sight seeing.

Just seeing Chani's response in regards to the monkeys. I hadn't heard about them before. Another interesting animal that people from North America tend to be interested in is the storks, which we do not have in the "new" world. I don't know if they are migratory, so gone in the winter, but, there are many storks in Alsace, they have been reintroducing them to the region.

Storks are migratory, they fly south to Africa for the winter. You won't see them in January. They are the trademark of Alsace, and they are HUGE.

I can't remember why they are so beloved in Alsace, I just remember a tour guide telling me about it LOL. BTW there are no storks in Strasbourg, but they were nesting in every other place in Alsace. I've also seen them in Spain and I've heard there are many in Budapest too. We see them here when they migrate, spring and fall. I saw a few stragglers heading north at the end of March near the Sea of Galilee.

I suggest Obernai both logistically and architecturally.

Eguisheim is a very picturesque little town, lovely to walk around. It has two churches, each with a stork's nest on top. The storks are treasured there, and after nearly becoming extinct because of deaths on the flight south, they seem to have been saved by a plan by Alsaciens to keep the babies there for several years to train them to over-winter there, being fed by Alsaciens, rather than take the dangerous migrating flight. There's a small stork park on the edge of Eguisheim (hard to find) where they have just a couple of cages to keep the families there until their babies are trained not to fly away south. There's also a very large stork park near Hunawihr (north of Eguisheim) which is very informative and allows you to walk among them in lovely treed surroundings. They protect otters also and a threatened beed of hamsters. It's a great park, but I've only visited in summer and don't know whether it's open in winter.

Another possibly seasonal treasure is south of Eguisheim, maybe at Ungersheim. It is a wonderful Eco-Musee', a large collection of farmhouses, bought to save them from destruction where they'd been for hundreds of years and gathered together there. ( Ecomusee.alsace/en/ is the English website for that). We have twice spent hours there, wandering around, admiring all the old farmhouses or village houses and the many storks nesting there. In summer at least there are also demonstrations, like of making tea from acacia, I think, and giving samples. There are also farm animals, carthorses pulling carts, sheep and pigs in barnyard. We adults loved it and the wonderful old buildings and perhaps your medieval-loving son would too. Up the hill (mini-mountain?) behind Eguisheim, you can drive up and walk through ruins of three castles above the town.

Other towns along there are fascinating too, especially, as someone else mentioned, Riquewihr! It's a terrific area!

Laurel

Maryland