Ostia Antica
Some of the best Roman ruins are just outside the city of Rome. Though locals go to Ostia Antica for its beaches, you are better off stopping before hitting the shore. In town, you will roll into the best rubble this side of Pompei. You can get a sense of how people lived their daily lives in the remains of ancient apartments, while the amphitheater from Augustus' time lets you test out acoustics good enough for an emperor. The best way to get to there is by a local train, which leaves from Rome's Piramide station, and takes about 30 minutes. After getting off at Ostia Antica's station, use the blue footbridge to cross the road and walk down Via della Stazione di Ostia Antica until you see an entrance on your left.
Tivoli
The gardens at Villa Gregoriana in the town of Tivoli were restored just a few years ago to their past glory — as they were when 17th- and 18th-century artists like Nicolas Poussin and Jean-Honoré Fragonard drew inspiration from them. The vertical garden is indeed made for romantics, winding through wooded paths, natural grottoes and ancient ruins. It all finishes at a stunning 350-foot waterfall. There are both convenient train and bus departures from Rome every hour. The central Termini train station and the Cotral bus station at the Ponte Mammolo metro stop provide service that will bring you close to the entrance to the gardens. By car, take the Via Tiburtina (SS5), the city's ancient road that heads eastward.
Orvieto
This little city perched on a rock in southern Umbria offers all the best of small-town Italy, perfectly preserved for modern travelers. Amble through Etruscan ruins on the outskirts of town. Wander the cobblestone center, which is closed to cars. Indulge in locally made wine and cheeses and crafts. Tour an 11th-century city hall and 13th-century gothic basilica. Also, the city is a charter member of Italy's "Slow Food" movement, and is indeed a great place to slow down. And eat. Try lunch at the Trattoria della Grotta on Via Signorelli Luca.
Most (but not all) of the trains bound from Rome to Florence and Milan stop at Orvieto. The train station is below the historic part of the town, but a regular shuttle bus will take you up the steep road to the scenic center. You can also drive up Italy's main arterial highway, the A1, exiting at Orvieto.
Terme dei Papi Spa
The city of Viterbo is itself worth a visit, but the nearby Terme di Papi Spa is the real reason to go. Hot springs that once helped Roman pontiffs kick back after a stressful conclave are a great place for a heathen like you to relax. A seven-mile wide fracture in the earth's crust allows hyper-thermal waters (up to 130 degrees F), rich in sulphurous salts and calcium bicarbonate and magnesium, to bubble up and soothe you. The quickest way to arrive is by car: Take Via Cassia bis (SS2bis) to Vetralla, then head east toward Viterbo, exiting at Viterbo Terme. There is also a bus that picks up passengers in Rome at Piazza Mancini and Corso Francia.