The area is called Ploce. For rooms view some of the accommodations we offer on our guide (Apartments Bilicic and Villa Adriatica have view over the Old Town, Apartments Amoret, Apartment Jelica are inside the Old Town).
There is no train station in Dubrovnik. The closest towns are Split and Ploce. You can take the train to Split and from there you can travel by bus (timetables and trip duration are on our guide).
If you have any other questions please ask.