Yes, we do like trains, but we are in our eighties and find that managing luggage on and off trains has become more difficult. We will have a car in Nice, and then plan to drive to Farnese (Italy) but we would like to avoid the very expensive drop-charge, if possible.We welcome any suggestions.
I don't know much about bus travel from Nice, but generally in Italy, the buses are not like the US greyhound system. It is mostly used for short- or intermediate-range transportation. You could probably find a bus that will go to Northern Italy from Nice, but it's unlikely there'd one that will go all the way to Lazio.