Bear with me; this is much easier to do than to write out.
This is the English-language Deutsche Bahn web site, by consensus an excellent source of rail info for all of Europe: http://www.deutschebahn.com/en/start-en.html . It's fairly forgiving if you use the English names of cities.
And here is the English-language Tren Italia web site, for Italy: http://www.trenitalia.com/tcom-en . Tren Italia requires you to use the Italian spelling for city names.
For this purpose, Tren Italia may be better; I'm not sure DB lists all the slow trains.
Enter origin and destination. Pick a date not too far in the future (so the regional trains are included among the options) that's the same day of the week as the September day you'll be traveling. Remember that the date must be entered in day-month-year order. Indicate one-way if there's a way to do that. Pick a time early in the day. Search.
Multiple options will come up. Some will be faster and more expensive than others. For maximum choices of stopping places (without transfers), choose one of the slow itinerary options. The faster trains make only a few stops. Now you need to expand the itinerary to see all the stops. On Tren Italia, you click on the little "i" in the lower right corner of the box listing the name and number of the train. You'll need to do that for each train that's part of the itinerary you're looking at.
To see stops on the DB website, click on the small red box with the right-facing arrow. That brings up the connections. Now click on the gray box with the arrow at the bottom of the list of connections. It's labeled "Show intermediate stops".
When I tested Rome-Como, TrenItalia initially gave me only options starting with the fast Freccia trains. If you want to see all the potential stops on the slow trains (which don't always take the same path as the fast trains, even aside from the fast trains' blowing through a lot of stations without stopping), click the "Regional trains" box just above the list of trains. Click all the "i's". That's a full list of all the stops on the interminable all-regionale trip from Rome to Como. At least for this route. The names I'm familiar with that pop up are: Civitavecchia, Tarquinia, Orbetello, Grosseto, Livorno, Pisa, Viareggio, Piacenza, Monza, Milano, Florence, Bologna. I've only been to the places in bold. No doubt others can comment on the desirability of visiting at least some of the others. I believe there are important Etruscan sites around Tarquinia.
If you take a map of Italy and sketch in lines through these places (there are two rail lines involved, the regionale veering west through Pisa while the faster trains hit Florence and Bologna instead), the places fairly near those line are probably reasonably accessible with a transfer, though the transfer might be to a bus.
Once you decide on a few places you might be interested in, go back to Tren Italia and search for those specific destinations to see how long the trips would be. I definitely love Orvieto, Siena and Assisi, but they are a bit off the main line. If you decide you must really minimize time on the train, there's a lot to see in highly-accessible Bologna, and it has a very, very large historic district. But it's a major city, certainly not a "cute Italian town", if that's what you're interested in on this trip. And of course Milan is also worthwhile but also very large.
