During a week's stay in Toulouse next month, I hope to make several day-trips by train to a couple of smaller neighboring towns. I am not sure I will have the energy to visit too many, so I am hoping to establish a list prioritizing the must-see destinations and ending with the ones it would be okay to skip. In my travels I put a premium on the a) scenic/picturesque qualities of the town itself, followed by b) its cultural offerings and c) gastronomic interest. The following order is provisional; please correct it if you think it could be improved. (ATTN: JoLui)
First choice: Albi (Toulouse-Lautrec museum)
2nd choice: Castres (Goya museum)
3rd Montauban (Ingres museum)
Last. Foix
Is there another wonderful town/village a short train-trip away from Toulouse that I am missing?
(I already know Carcassonne, thank you.)
I like your order; I'dperhaps prioritize Foix over Montauban. I have never been to Castres but it looks more interesting than Montauban, where I've only been for work once and have not been impressed (but did not visit the museum). I'd take Cahors over Montauban, but the train ride is longer and less frequent.
As for Foix, it has a beautiful castle. Not much else (you can see the rest of the old town in 45 minutes), but it is a very different flavor than Toulouse.
Near Foix is the town of Mirepoix. Its medieval central square is a delight.
Going the other direction Pau would a good day trip. The chateau is full of history.
Honestly, all the places you mentioned are worth a visit. Seeing the diversity between them, given that they offer completely different atmospheres, cultures, architecture, landscapes, and even food, could be a good reason to visit them all.
Since you won't have a car, I don't really have anything to add. Within an hour of Toulouse, there are plenty of Bastides (medieval villages), but without a car, it's too complicated. Perhaps Gaillac if you're a wine lover (often better wines than Cahors). It's halfway along the Toulouse-Albi train line.
Also keep in mind that in all these towns, the SNCF train station is located outside the historic center. You won't just have to cross the street to get to museums or other interesting places. It's often a 20-minute walk through an area that's mostly uninteresting.
Note that the Occitanie rail network, liO, offers unlimited travel passes for 2 to 6 consecutive days.
https://www.visit-occitanie.com/en/rail-tour/
Click on the map at the bottom of the page for more information on possible train destinations. Everything is detailed, even the best seats for a better view.
The Bastides line I mentioned is suggested there, but as you'll see, a journey via this train line with stopovers can take up to 9 days...
You may sometimes be able to get a reduced admission price at museums by presenting your train ticket (particularly in Castres and Albi), but I don't know if this applies to passes.