People often think of Vatican City as part of Rome, but it's really a separate entity. Vatican City can easily be visited as part of a Rome vacation. Saint Peter's Square and Basilica, the Sistine Chapel, and the extensive Vatican Museums are the main sites. Plan to spend at least half a day.
The Via Appia Antica, old Appian Way Road, was the major road of the ancient Roman Empire. It's now a regional park, Parco Regionale Dell'Appia Antica, and there are several catacombs to visit. From Rome, take bus 118 or 218 to get to the catacombs of San Callisto, the largest and most impressive of the catacombs. From there you can walk or bike along the ancient road, lined with tombs and churches. A beautiful place for lunch on Via Appia Antica is the Cecilia Metella Restaurant, especially when it is nice and you can sit on the patio, or pack a picnic. Sunday is the best day to go when much of the Appian Way is closed to traffic.
The ruins of the ancient Roman port of Ostia Antica are well worth a visit. You can easily spend several hours wandering around the old streets, shops, and houses of this huge complex that generally sees far fewer tourists than Pompeii. To get there, take the Metro Line B to Piramide or Magliana and take the Ostia Lido train from there.
In Tivoli, you can see the villa, gardens and fantastic fountains of the Renaissance Villa d'Este, built in the 16th century. Then take a short bus ride to the extensive grounds of Hadrian's Villa, created by Emperor Hadrian in the second century and now a UNESCO World Heritage Site. East of Rome, Tivoli is accessible by train from the Roma Tiburtina Station or by bus. Tivoli Map and Guide
Perched atop tufa cliffs, the Umbrian hill town of Orvieto makes an impressive sight. Inhabited since Etruscan times, Orvieto's monuments and museums cover milleniums of history. Orvieto's stunning duomo (cathedral) with its mosaic facade is one of the best medieval monuments in Italy. There are plenty of shops and restaurants where you can try specialties of the Umbria region. Orvieto is a little over an hour from Rome - see how to get from Rome to Orvieto. A funicular connects the station and lower town with the medieval center above.
Tarquinia is known for its Etruscan tombs just outside town and its excellent Etruscan Museum. The town also has a medieval center and the Cathedral has good frescoes dating from 1508. Tarquinia can be reached by train on the Roma-Ventimiglia line in a little over an hour. Trains leave from Roma Ostiense station but some trains also depart from Termini or other Rome stations as well.
Frascati, in the hills 13 miles from Rome, is part of the Colli Albani and the Castelli Romani area, a volcanic complex of hills and lakes where well-to-do Romans have had summer homes for centuries. Frascati is a pleasant wine town and a good place to escape the summer heat of the city. Other Castelli Romani to visit as day trips include Grottaferrata, Marino, and Castel Gandolfo, home of the Pope's summer palace. These towns can all be reached by train.
If you're in Rome and want to escape the heat of the city, the closest place to go is Ostia Lido. While it might not be as glamorous as some of the other Italian beaches, it has some nice private beach areas available for day use. If you want to go a little farther, there are good choices both north and see. You'll find directions for getting to three beaches from Rome on public transportation with the link to A Day at the Beach above.
If you take one of the very fast trains, it's possible (although somewhat expensive) to reach Florence from Rome in one hour and thirty-nine minutes - see how to get from Rome to Florence. Florence's historic center can be reached by walking from the station. Although there's lots to see in Florence, you can get a good overview in one day.