From Italy:

From Milano Centrale, you can reach Como San Giovanni FS by train (timetable: Trenitalia). Then, you can reach Menaggio with public transport.

From Milan, you can also take the train service run by Ferrovie Nord  from Cadorna train station (undergoround service, MM1 and MM2) to Como Lago (timetable: Ferrovie Nord Milano).Then, you can reach Menaggio with public transport.

From Germany:

Lugano is the nearest train station to get to Villa Vigoni from Germany (timetable: Deutsche Bahn). Then, you can reach Menaggio with public transport.