Milan or Lake Como?

If you only have one day and Milan is your arrival city, i would stay in Milan. Fashion capital of Italy and the girls could easily spend an entire day if they are interested in fashion. You could all spend time at Galleria Vittorio Emanuel II along with the Duomo. Plus lots of other good sights and gelato.
Going to Lake Como and back will cost most of a day with little chance to see much.

Ann consider the need to get over jet lag.

We were just in Lake Como this past May, and didn't want to leave; it was our second visit. We shall return.
However, I'm trying to gain the perspective of teenage girls, hmmm.
What time of year? If this is the day you land , then jet lag must be factored in, and Id say the travel is too much. Where are you staying the night before? It's an hour regional train to Varenna in Lake Como, and then the 20 minute ferry rides to Menaggio and Bellagio. To return, repeat. These are beautiful lake towns with unique shops and beautiful gardens and villas to explore.
Milan is a commercial city, the highlites being the church/ rooftop of the Duomo , and the Last Supper, ( if someone is dedicated enough to get the tickets.) Of course, Milan is high-end shopping, which may be beyond the girls' budgets.
What are the girls interests? The two areas are very different.
I'd say give the girls a week to do their own research, then take a vote. They need to have buy in.
Kudos for being brave enough to take a group of teenagers to Italy! Safe travels.

Knowing just where in your itinerary this day is would be helpful.

Would you be spending the night in in one or the other or simply passing through during the day?

Stay in Milan. It is like Emily in Paris meets the Devil Wore Prada. The girls will be totally bored in Lake Como. I’ve been to both places. Loved them both but Milan is exciting. Lake Como is sedate and things to see and do were spread out. Everywhere you turn in Milan someone looks fabulous with an accessory, jacket, athletic shoes- it was amazing and inspiring. It’s fun going into the high end shops to look around. For example, I believe the flagship Prada store is in the Galleria by the beautiful Duomo. I saw stuff in Gucci that was amazing. I didn’t buy anything but I appreciated the opportunity to see and visit luxury goods stores without being judged.

I think you moms and the girls will have a blast.

What time of the year?

In August only the notorious brand fashion stores will be open in Milan and the Navigli district will be very quite. The "petrified forest" on top of the Cathedral could be too hot to enjoy the views.

Italians grow up in Italy, I have heard Milanese say that the Borghese Gallery is overrated and that Brera is more important for Art History... I don't know much about US teens, but I hope they can get the pure beauty of the lake even if they would rather being shopping in Milan.

More, you can leave them alone for a couple of hours on the Lake. I wouldn't do the same in Milan on their first day in a foreign country. Not in August.

Thanks for all your help and insights everyone!

We are going in mid September, taking the girls out of school. I think some of them are more interested in Lake Como just because it's so scenic and it's a different type of scenery than anywhere else in Italy. I doubt the girls would be more interested in shopping in this instance since the stores are so high end.

Also, yes, it's our first full day in Europe and we are definitely worried about jet lag. Exploring Milan for the day would possibly allow a more relaxed and lazy day, but with such a special once in a lifetime trip I also hate to throw a full day away. We did schedule a long layover in London on the way so we would have had one full day to adjust a bit already by that point.

In some ways, I feel like riding on ferries or a boat on a lake and sauntering around little villages or villa gardens sounds relaxing and easier for jet lag than walking longer distances in a big overwhelming city all day. But then again we will have been on a plane for the entire day and a half prior so walking a lot might feel lovely.