The colonial centre around the Parque Duarte and the Calle del Sol is compact and walkable. The Monumento is at the eastern edge of the centre — a 15-minute walk uphill from the cathedral, or a short taxi ride.
For longer trips within the city, conchos (shared taxis running fixed routes for a few pesos) cover most main avenues. Regular taxis are cheap by international standards but should be hailed by phone (Apolo, Aero) rather than from the street. Uber operates in Santiago and is the easiest option for visitors.
Renting a car makes sense if you plan day trips into the Cibao mountains or to the north coast. Driving in central Santiago is chaotic but the highways out of town are good.