Did Campania/Puglia down to Calabria and back last month and Veneto-Emilia Romagna last year.
Others have covered Trieste down to Lecce. I would go via Ravenna (roman mosaics). In Emiglia Romagna local trains need the Trenitalia planner, they are not fed into international ones.
+1 for Taranto, old town is very Italian mix of crumbling next to renovated.
Between Reggio di Calabria and Lamezia Terme Centrale some regionals serve the original coast route via Tropea, better scenery than the direct tunnel.
Amalfi coast: rather than skipping it by train I would use bus Salerno-Sorrento, there is a bus day ticket so you can break journey anywhere. Avoid summer. Sorrento-Naples break at Castellamare for the Faito cable car and view from 1100m.
Napoli to Rome: the 'coastal' route only touches the coast at Formia. I don't know north of there until Genoa.
Tickets overall: as you want to linger there is no single answer. You will need a mixture of everything, Frecce, Intercity and regional. Some bits have near-hourly fast-ish regional services, others almost none, e.g. Termoli-Foggia. I would compare Interrail n days in m months + reservations (Eur13 for Frecce) with fares on Trenitalia to choose. If using regionals for a spell of 3 or more days 'Italia in Tour' is Eur30/3 day, Eur50/5 day, no time restrictions, TI+TTPER but not others (TUA in Abruzzo, FSE beyond Bari) and is not valid in the Cinque Terre.
... given the hilliness visitors might well need to use the buses to get around too - but there's no city bus map published ...
Bus map (AMT is the city transport operator):
Funicular and lifts are vital in Genoa even if you don't need buses. Starting point
» Rete e Orari |
www.amt.genova.it