Last fall we flew into Rome, took the train to Orvieto, and from the train station took the bus to Piazza della Repubblica. It seemed like the bus sort of met the train, so don't dilly-dally in the station except to buy bus tickets. I don't remember cobblestones being a problem, at least, they were not the really rough or bumpy ones there are in some towns.
After four nights in Orvieto we took the train to Perugia. We thought we knew we had to change trains "in Cortona" and so we actually missed the correct station to change because the station is signed as Terontola or at one point Terontola-Cortona. We assumed there'd be another station marked just plain "Cortona," but nope. Had to backtrack.
From the Perugia train station, it's a very brief walk to the mini-metro station on a direct and obvious sidewalk. Lots of people will be walking that way. Our American credit card worked fine in the machines here and everywhere else. The streets were pretty smooth in Perugia in the center of town. My suitcase does have large wheels and only two wheels, so I may not notice the bumps as much as people with 4-wheeled spinners.