To have the train take you to a station and then walk to a mountain in just one hour? I think there are very few such starting points in Slovenia... But you can travel nicely (and cheaply!) by train to stations that are excellent starting points for mountains... Of course the problem is that on weekends trains on certain sections run rarely or not at all. Such example is Sežana - Nova Gorica, Ljubljana - Kamnik etc... If we start in Sežana towards Ljubljana first station Povir (starting point for Stari Tabor 1.30 hours), Divača (Vremščica 3 hours), Gornje Ležeče (Vremščica 1.30 hours), Košana (Vremščica 1.30 hours, Osojnica 3 hours), Pivka (Osojnica 1 hour, Sv. Trojica 3 hours, Šilentabor or Tabor nad Knežakom 1.30 hours), Prestranek (Osojnica 2 hours, Sv. Trojica 3 hours), Postojna (Pečna Reber 1 hour, Sv. Trojica 4.30 hours, Nanos 6 hours), Rakek (Slivnica 3 hours), Planina (Planinska Gora 3 hours), Logatec (Kališče 3 hours), Verd (Pokojišče 3 hours), Borovnica (Pokojišče 3.30 hours), Preserje (Krim 3.30 hours)... From Ljubljana towards Zidani Most first station Laze (Janče 2 hours), Jevnica (Janče 1.30 hours), Kresnice (Geoss 1.30 hours), Sava (Zasavska Gora 2.30 hours), Trbovlje (Mrzlica 3 hours, Kum 4 hours), Zagorje (Kum 3.30 hours), Hrastnik (Kum 3.30 hours, Mrzlica 3.30 hours), Zidani Most (Kum 3.30 hours, Vel. Kozje 3 hours, Kopitnik 3 hours)... And towards Zagreb from station Radeče (V. Kozje 2.30 hours) Loka (Lisca 4 hours), Breg (Lisca 3.30 hours) Sevnica (Lisca 3.30 hours), Blanca (Bohor 3.30 hours) Brestanica (Bohor 3.30 hours)... And towards Maribor Rimske Toplice (Kopitnik 2.30 hours), Laško (Šmohor 2.30 hours), Celje (Celjska Koča 2.30 hours), from Štor or Šentjur to Svetina about 2.30 hours, Dolga Gora (Boč 3.30 hours), Poljčane (Boč 3 hours)... And towards Jesenice among others nice starting point Žirovnica (Stol 5 hours)... From Nova Gorica towards Jesenice Solkan (Sabotin 1.30 hours, Sv. Gora 2 hours), Plave and Kanal (Korada 3 hours), Grahovo (Rodica 5 hours), Hudajužina (Porezen 4 hours) Podbrdo (Porezen 3.30 hours, Črna Prst 3.30 hours), Bohinjska Bistrica is excellent starting point for Julian Alps...
I think Karletto has already got a car... True though that trains mostly run on weekdays, on weekends less frequently... Slovenian Railways aren't that dumb to run empty trains waiting for someone who goes to mountains by train twice a year... I did most of my trips by train a few years ago - and it was nice and still is... Greetings and enjoy your trips and mountains!