No mountains exist within Rome's city limits. Rome sits on the Tiber River in the central Italian peninsula, built on seven historic hills (Palatine, Aventine, Capitoline, Quirinal, Viminal, Esquiline, Caelian)—which are hills, not mountains (max elevation ~75 m / 246 ft).
The nearest true mountain range is the Apennines, ~100 km (62 mi) to the northeast. The Alban Hills (Colli Albani), a volcanic complex with lakes (Albano, Nemi), lie ~20 km southeast—peaks ~950 m (3,100 ft), but outside the municipal boundary.
Romans escape to the Apennines (Terminillo, Gran Sasso) or Alps for skiing/mountaineering. In the city, the "hills" provide the only elevation.