One of the best ways to see a country and its countryside is to take an inter-city train. Italian trains are pretty comfortable and quite timely, but do not expect anything more than that.
Depending on the destination, connections can sometimes be a little awkward. So plan wisely!
As the train whizz past the buildings in the towns, along the coast and plains or through the mountains, have a camera ready just in case you come across something photo-worthy!