Monteverde is the Rome that tourists never reach: a calm, well-off hill above Trastevere where the city stops performing for anyone. The reason to come is the green at the top of it — Villa Doria Pamphili, the largest park in Rome, big enough to lose an afternoon in.
Climb up from Trastevere station through Via di Donna Olimpia and the interwar blocks of Monteverde Vecchio, then enter the park from its eastern gate. Inside, the trick is to keep walking west, away from the entrances, until you have the umbrella-pine avenues to yourself. They were laid for carriages and they still feel processional.
The middle of the walk is the Casino del Bel Respiro, the garden villa with its box parterre, and the ornamental lake below it with the folly arch and the turtles. Find a bench by the water; this is the stop. Then come back down the hill through the quiet upper streets around Villa Sciarra — downhill the whole way to Trastevere station and the regional train back into town.