Coming from Milan by a train and using a public transport during 2.5 days trip around Lake Como
Would like to visit: Bellagio, Varenna, Menaggio, Lugano
Which town is the most convenient to stay in?
Como, Varenna, Menaggio
Varenna, Menaggio and Bellagio are across each other on Lake Como and are connected by Ferry that goes across all three. As such it doesn't make much difference. Varenna has the advantage of having the train line running along the eastern shore, therefore is more easily reached by train. But from Varenna you can go to the others by boat easily. And both Bellagio and Menaggio are connected to Como via bus and boat.
Lugano however is not on Lake Como, it's on Lake Lugano in Switzerland. If Lugano is of interest to you, then the best base is probably Menaggio, because there is a regular bus that goes back and forth from Lugano and Menaggio in less than one hour:
http://www.menaggio.com/ita/e-lakes/Orari_bus.pdf