I haven't been on a tour with Walks of Italy, but they have been recommended by others on this forum. Seems like several possibilities for you and son.
I'd suggest staying in the area of the Piazza Navona, Pantheon, and Trevi Fountain. Very central and walkable, lots of street life and restaurants. Trastevere would be another option, a little quieter and more "residential" in character without being too far from the main sights.
I'd assume a teenager is less interested in museums (like the Borghese or Capitoline) and maybe more in where things actually happened (like the Colosseum and Forum). Ostia would be worth visiting if he likes ruins (a whole city). I expect the Appian Way might also appeal (I haven't been there). You can bike along it.
The one thing I wouldn't miss is St. Peter's Basilica. Even if he's not into churches or art or museums, this building has by far the world's largest masonry dome, and he will see pictures of it for the rest of his life. Not to be missed, even if you don't spend time in the Vatican Museum.