We think you shouldn’t miss to visit the archaeological gem of Ostia Antica, at a neighborhood of Rome near the seaside that you can reach in about half an hour by train. Here the website.
You can also have the opportunity to enjoy the night openings of the Vatican Museums on the 25th September (every Friday) and the musical accompaniment. Be sure to make reservation on the official website, where you can find the program and other info.
For the beautiful scenery, we suggest the classical music concerts at the Theatre of Marcellus (14th September: Schubert and Chopin played by the pianist Rossana Lanzillotta; 15th September: Paganini and Bach played by the saxophonist Isabella Stabio; 25th September: Haydn and Bartòk played by the two violinists Giulio Menichelli and Samuele Michele Cascino). Visit thewebsite of the organizing association for further info. For music concerts we also recommend to check the program at the Auditorium Parco della Musica.
Finally, we could suggest the two special events series entitled “Journeys through Ancient Rome: 2 stories and 2 routes”, running every evening in two places: the show at the Forum of Augustus at 9.00 pm – 10.00 pm – 11.00 pm and the show relating to the Forum of Caesar taking place at Trajan’s Forum every 20 min between 9.00 and 12.00 pm. More info on the official site.
Feel free to ask us more info if you have specific requests or need practical details.
Hope this helps!