Tivoli is all about its three great villas, each quite different in character: Hadrian's Villa Adriana sprawled across the plain below town, the Renaissance Villa d'Este with its hydraulic gardens, and the wild Villa Gregoriana built around the Aniene waterfalls. You can see two in a full day; all three requires either an early start or a second visit.
The old town itself adds a couple of hours — the cathedral, the Romanesque churches, the surviving Roman ruins of the Sanctuary of Hercules Victor and the Mensa Ponderaria, and the Rocca Pia fortress at the southern gate.