Put yourself in a different position and see the city from a different perspective.
It’s obvious you can’t miss Piazza San Pietro or il Colosseo. But it’s great if you try to discover what’s between them.
Start from Piazza Venezia and look for Piazza Mattei and its beautiful Fontana delle Tartarughe. Then go on to the Ghetto (enjoy the real Jewish Sweets at Pasticceria Boccioni, and the roman Pizza BIanca at Antico Forno Urbani in front of it).
The cross the river on Isola Tiberina and walk around Trastevere: don’t forget to visit Santa Maria in Trastevere. Cross Ponte Garibaldi and enjoy Via Giulia. When you want turn right and get back to Piazza Farnese, Campo dei Fiori, Piazza Navona. Possibly walking outside the big tourists stream: just choosing the street next to the crowded ones you find yourself deeply into the city. And don’t worry, the city is safer then they tell you.
If you go to Santa Maria Maggiore, and I think you should, then go to Santa Prassede; it’s close and has an astonishing golden mosaic, completely covering a room. Don’t miss it.
San Luigi dei Francesi (Il trittico su San Matteo), Santa Maria del Popolo (La Conversione di San Paolo e la Crocefissione di San Pietro), Sant’Agostino (Madonna di Loreto, o Madonna dei Pellegrini): visiting these three churches you can see 7 beautiful Caravaggio paintings. This is something that only in Roma can happen! And if it’s not enough for you, you can visit Galleria Doria Pamphilj, Galleria Borghese, Palazzo Barberini, Musei Capitolini, Palazzo Corsini and Musei Vaticani to complete with other 14 masterpieces of Michelangelo Merisi (aka Caravaggio….).