The ability to tailor the properties of semiconductor nanocrystals through creating core/shell heterostructures is the cornerstone for their diverse application in nanotechnology. The band-offsets between the heterostructure components are determining parameters for their optoelectronic properties, dictating for example the degree of charge-carrier separation and localization. So far, however, no method was reported for direct measurement of these factors in colloidal nanocrystals and only indirect information could be derived from optical measurements. Here we demonstrate that scanning tunneling spectroscopy along with theoretical modeling can be used to determine band-offsets in such nanostructures. Applying this approach to CdSe/CdS quantum-dot/nanorod core/shell nanocrystals portrays its type I band structure where both the hole and electron ground state are localized in the CdSe core, in contrast to previous reports which predicted electron delocalization. The generality of the approach is further demonstrated in ZnSe/CdS nanocrystals where their type II band alignment, leading to electron-hole separation, is manifested.