These are two areas that I'd like to see when in Italy this September. Does anyone know if there are easy train connections to these places from Rome?
Castelli Romani is not a specific place. It encompasses several municipalities. Not sure where you want to go.
They can be reached by either buses (CO.TRA.L) or in some cases by train (e.g. Castel Gandolfo, Albano Laziale, Frascati). Lago di Nemi has no train service (only bus).
You may be able to get close by train but Roberto is right. You'll have to take buses the rest of the way.