Santa Cruz is built around concentric ring roads called anillos. The historic center within the first anillo is compact and walkable, but beyond that the city sprawls and you will need transport.
Local buses are cheap and cover most of the city, though the driving is aggressive — hold on tight, as they stop and start without warning. If you speak some Spanish, people at bus stops are happy to point you in the right direction. Taxis are plentiful and affordable for getting across town. The outer anillos are still growing and not all roads are paved, so expect dust and bumps on the fringes.