Local electronic properties of InAs/GaAs nanostructures are studied using a real-space moments method sp3d5s* tight-binding approach. The order (N) method is unique because it allows for accurate and highly resolved determination of local density of states that accounts for local strain, disorder, and defects, without diagonalization of the full tight-binding Hamiltonian. The effects of free surfaces and strain are first investigated by considering pure, cuboidal GaAs nanostructures. The quantum confinement in an embedded InAs quantum dot is then shown directly through the local densities of states projected on different atoms in the structure. The relationship between effective energy band gap and quantum dot size is mapped onto a simple equation. Finally, the real-space study is applied to quantum dot structures observed experimentally using scanning tunneling microscopy. Atomic positions are obtained from the images and used as input into the tight-binding calculations in order to study interfacial effects on the local electronic structure of real embedded quantum dots.