Hey Anne-Meike,
unfortunately train traveling in Croatia isn’t that much fun, as many places are not reachable by train or only with slow trains and few connections per day.
I would recommend you:
Plitvice Lakes (must see), Dubrovnik (liked it way more than Split), Istria, maybe visit an island near Split? There are also some smaller beautiful cities near Split.
Zadar and Sibenik are also worth a visit in my opinion.
enjoy your trip!
Thank you very much for all the information! We will visit those places you have mentioned :)
Although our travel was many years ago, we thoroughly enjoyed visiting the beaches, food and the ever present fragrance of lavender, on island of Hvar off the coast from Split. I believe it is still accessible by ferry from Split.