Things may have changed since we last visited Salta in (I think) 2019. We did everything by public transport and used tours organised on the spot when we were in the city though you would probably have more flexibility if you were using your own car. There's lots to see and do in Salta without even leaving the city - check out the local guias touristicas and look out for concert programmes and other performances - Salta is quite a centre for culture. Oh. And I hope you like dogs...
The Tren a las Nubes tour starts from the railway station in Salta at some unbelievably early time in the morning but, unless it's changed, you will be getting onto a bus outside the railway station and traveling under escort to San Antonio de los Cobres where the train trundles some 20km or so up to the viaduct and then trundles back down again. The bus takes you back to Salta by evening and it is a full day excursion. The train stops at various miradors along the way and there's never a shortage of people offering to sell you souvenirs at those points but there are no other stations or towns that I recall on the train route. There are hotels and hospedajes in San Antonio de los Cobres so if you were travelling independently you could probably stay there overnight and just pick up the train from there. I say probably - I've not done that so check it out for yourself first. The route from Salta to San Antonio is pretty remote so you need absolute confidence in your vehicle - which is one of the reasons why the official trips have an escort for the tour bus. One of the other reasons for the escort is preparedness for a medical emergency: it really is at a very high altitude and although a day or two spent beforehand in Salta will help you aclimatise, some people struggle in the thin air.
There are other day trips you can organise from Salta. I believe there's one to Cafayate which is a wine producing area (if you haven't already drunk them yet, you'll have seen Cafayate wines in the supermarkets. There are experts on this forum who can tell you much more about these wines than I could but suffice to say they are quite different from the wines produced in the Mendoza region. We didn't do the day trip from Salta, we made our own way to Cafayate and stayed overnight and enjoyed it.