On a budget, Day Trip to Tivoli (Villa d'Este & Hadrian's Villa) still earns its price.
€90–150 pp (tour) / ~€25 DIY
Two UNESCO sites in one outing: Villa d'Este's terraced gardens are a riot of hundreds of fountains, and Hadrian's Villa is a sprawling imperial estate to roam. They're a few km apart and reaching both by public transport is fiddly, so a tour or car makes the day far smoother.