General rule of thumb is trains in the Balkans are slow as hell and sometimes the bus is better. In fact I believe Croatia does not have a well developed train infrastructure so its probably a train to Zagreb then a bus to Dubrovnik.
Rome - Venice ...half to a full day depending on if you want the fast train or the slow train...you can see the times on the trenitalia website
venice - vienna...night train
vienna - dubrovnik...maybe a train plus bus
dubrovnik - budva...judging by the map, half a day
budva - belgrade....seems like a night train or night bus
belgrade - budapest...7 hours...can be done in the day or night
budapest - krakow...I recommend the bus...its cheaper and faster, but can be done on the train
krakow - prague...night train but may also be cheaper/faster by student agency bus
prague - berlin...can be done in half a day
berlin - brugges...unsure but I think this is a night train
brugges - brussels...a few hours
brussels - london...If you're doing the eurostar thats like 3 hours
Hopefully my hostel will be open sometime btwn the middle of May to the beginning of June. I will keep you and the boards updated. Lets just say the property I have lined up is pretty sweet