We study the electronic properties of spherical quantum dot quantum well nanocrystals within a symmetry-based tight-binding model. In particular, the influence of a concentric monolayer of HgS embedded in a spherical CdS nanocrystal of diameter 52.7 A is analyzed as a function of its distance from the center. The electron and hole states around the energy gap show a strong localization in the HgS well and the neighboring inner (core) interface region. Important effects on the optical properties such as the absorption gap and the fine structure of the exciton spectrum are also reported.