You know, I don't know if I ascribe to the 'train stations in seedy areas' thing. We are considering taking a couple dear friends with us to Europe, and want to travel Munich-->Hall in Tirol (Austria)-->Verona-->Florence-->Rome, all by train, and if possible staying within walking distance of the stations.
Well, maybe not by Roma Termini, but I do think that area is fine, really funky with plenty of attractions (Baths of Diocletian right across the street), and truth is to go almost anywhere in Rome, you have to funnel through Termini anyway, which to me is a real rogue's gallery & great people-watching spot besides being a wonderful transportation hub. So that's a maybe. The Florence SMN area is fine, and I still have to research the others.
But to our friends I want to illustrate how efficient that kind of travel can be. The Hall to Verona leg is over 4 hours, but everything else is around 90 minutes. You walk to the station, ticket in hand, and you step on and grab your seat. No security, no jetway, easy peasy. When we've done this in the past--we did Paris to Salerno over 17 days--we scheduled our trains to leave late morning and arrive mid-afternoon, boom, a block or so walk, we're checking in to our hotel. Never felt rushed, treated the travel by rail as an adventure, packed a picnic each time, brought great reading material, dozed & looked out the window, and just enjoyed the hell out of it.
And oh yes--I would insist to our friends, as we've learned--not to have anything larger than a 21" spinner that can be hoisted & slid into an angled overhead rack on the train. Saw many examples of train riders struggling mightily with large suitcases--not worth it. As others have said, I could live indefinitely out of my 21" Samsonite.