Trastevere: Bars, restaurants, and small shops. Basilica di Santa Maria is a beautiful site! You will see Isola Tiberina (a little island in the middle of the river), a historic hospital in the city. Walk to Monumento a Giuseppe Garibaldi where you'll have an incredible view of the city, including the mountains outside the city! A bit further out is Monteverde, less traveled by tourists and has very good local restaurants for a good price. Campo de Fiori: A rectangular area south of the Pizza Nova known for its food market, shops and eateries. The Jewish Quarter, or "Roman Ghetto" is walking distance and also worth seeing. Testaccio: Monuments, churches and a large glass-roof market on a Roman archeological site with over 100 gourmet and fresh food stalls! Monti: A vibrant and unique area in the city. Portuense: Famous for the weekend market. Good restaurants are Ristorante Pecorino (GREAT carbonara), La Tavernaccia, and the wine bar, Palombi. Also visit the Baths of Caracalla.
Pizzarium: https://bonci.it/ Il Trapizzino: https://www.trapizzino.it/en/ Antico forno Roscioli: https://www.anticofornoroscioli.it/ Elettroforno Frontoni Ostiense: http://www.elettrofornofrontoni.it/
Ciampini: https://ciampini.com/ La Romana: https://www.gelateriaromana.com/ Otaleg: https://www.otaleg.com/
Fori Imperiali (archaeological site) Palatino (archaeological site) Pantheon (archaeological site/church) Castel Sant'Angelo (archaeological site/museum) Piazza di Spagna (no admission fee) Piazza Navona (no admission fee) Fontana di Trevi (no admission fee) Musei Capitolini (museum) Scuderie del Quirinale (museum) Palazzo Barberini (museum) Palazzo Corsini (museum) Basilica di San Pietro (church) Basilica di San Giovanni in Laterano (church) Basilica di Santa Maria Maggiore (church) Basilica di San Paolo (church) San Pietro in Valle (church) Santa Maria dell'Anima (church) Sant'Ignazio da Loyola (church) Santa Maria del Popolo (church) Chiesa del Gesù (church) Santa Maria in AraCoeli (church) Santa Maria in Trastevere (church) San Luigi dei Francesi (church) Santa Maria in Cosmedin - with Bocca della Verità (church)