I'm planning to do a day trip from Milano to Lake Como.
I will take the morning train to Varenna then the ferry to Bellagio, but I'm wondering if I should continue the journey to Como or head back to Varenna to take the train to Milan?
According to a friend, the ferry from Bellagio to Como takes you the most scenic part of Lake Como. Is that true? But I'm not interested in visiting the city of Como itself on such a short visit.
Heard it's a big city without the charm of Bellagio or Varenna.

Como is a small city, not huge, and has a nice small old town near the water. But not a priority for a day trip. Varenna and Bellagio are small villages. I did do the boat trip from Como up to Bellagio years ago so I don't really remember where exactly the best scenery is, but it's pretty damn good in the mid lake region. My most recent trip was a day trip from Milano and I took the train both ways to/from Varenna and then took the ferry to Bellagio and back. The boat trip down to Como takes a few hours, and are not all that frequent. I'd concentrate on the mid lake region if I were you.

What are your plans beyond Varenna and Bellagio? Unless you're really into shopping, wandering the two towns would hardly take up an entire day.

You could visit the castle ruins and falconry in Varenna. You could ferry to either Villa Balbianello or Villa Carlotta on the western shore of the lake. Depending on the time of year, there are beautiful gardens in several locations you could visit.

Or maybe a leisurely boat ride from Bellagio to Como sounds more appealing. It's really up to you. (FWIW, I think the scenery is more beautiful the farther you go north -- not south.)
You should do some research to find what interests you most.

You can get the ferry from Lenno which has a tiny ferry terminal. And our tour of Villa Balbienello was fantastic! Don't miss it. A famous scene in Casine Royale was filmed there as well.