day trips from Strasbourg by train

You could visit the lovely villages of Riquewihr and Ribeauvillé on one day using the local bus that takes you along the wine road from Colmar line 106, walk south to Eguisheim or take a taxi or hire a bike from just outside the train station, and you can visit the village of Turckheim either by bus (25 ... going on if you wish to Trois Epis in the mountains for the ride) or by train (and continue on up to Munster .. visit the Maison du Fromage and see the storks around the town hall and the attractive small shops).

Obernai and Kaysersberg are lovely towns as well and very close to Strasbourg. It's an easy day trip to either town via train.

The Black Forest train line connects from Strasbourg and an easy and enjoyable trip can be had. Excellent model railway along the way, pleasant scenery, bridges and gorges, and the very pleasant town of Gengenbach on the way or on the way back - that would do for me. Different country, too.

Definately the wine villages along the Route des Vins near Colmar, all the ones R.Jean lists. These are not accessable by train, you need a bus or renting a car.
See website: https://www.alsace-wine-route.com/

If you only want places accessible by train, then Freiburg im Breisgau, on the German side of the Rhine, and Basel, just inside Switzerland.

Heidelberg and Freiburg are options that are likely an easy short trip by train. (You said other than Alsace wine route).

If you are into rail or road transport, Mulhouse has the world class French national museums of cars and of railways. Otherwise it's not worth the trip.

The Rhine and the road along the Rhine with its stunning castles is nearby and a beautiful area. When we were in this area we did a 3 hours or so boat trip on the Rhine which was terrific. In 1960 I had driven along the Rhine in this area and remembered how beautiful it was and so 50 years later when we were in the area, I knew I wanted to see it from the water. I was surprised at how unchanged it was from my memories of it. This stretch of the Rhine is vineyards, beautiful towns and castles -- a great afternoon.

I don't know if you can access any of this without a car; I would not stay in Strasbourg for 5 days without a car. I don't think there are connections to the wine road by train either.