I took my son to Rome when he was 15; a bit older than your son but then I'd also taken him to other countries when he was younger.
We had a blast.
don't worry about travelling just the two of you, we never had any problems, and it was great to spend a holiday together.
All I would say is build in some kid stuff - while he has always enjoyed museums etc, it also helped keep him happy and relaxed to go and do some cheesy kid stuff too. I think we went here:
Time Elevator Rome 3-D Movie and Simulated Ride, Rome Attraction Tickets | Viator.com. the colosseum was a big hit too, along with plenty of gelato.