This dissertation presents results of a project bringing Scanning Tunneling Microscope (STM) into a regime of unlimited operational time at cryogenic conditions. Freedom from liquid helium consumption was achieved and technical characteristics of the instrument are reported, including record low noise for a scanning probe instrument coupled to a close-cycle cryostat, which allows for atomically resolved imaging, and record low thermal drift. Subsequent studies showed that the new STM opened new prospects in nanoscience research by enabling Scanning Tunneling Spectroscopic (STS) spatial mapping to reveal details of the electronic structure in real space for molecules and low-dimensional nanomaterials, for which this depth of investigation was previously prohibitively expensive. Quantum-confined electronic states were studied in single-walled carbon nanotubes (SWCNTs) deposited on the Au(111) surface. Localization on the nanometer-scale was discovered to produce a local vibronic manifold resulting from the localization-enhanced electron-vibrational coupling. STS showed the vibrational overtones, identified as D-band Kekulé vibrational modes and K-point transverse out-of plane phonons. This study experimentally connected the properties of well-defined localized electronic states to the properties of associated vibronic states. Electronic structures of alkyl-substituted oligothiophenes with different backbone lengths were studied and correlated with torsional conformations assumed on the Au(111) surface. The molecules adopted distinct planar conformations with alkyl ligands forming cis- or trans- mutual orientations and at higher coverage self-assembled into ordered structures, binding to each other via interdigitated alkyl ligands. STS maps visualized, in real space, particle-in-a-box-like molecular orbitals. Shorter quaterthiophenes have substantially varying orbital energies because of local variations in surface reactivity. Different conformers of longer oligothiophenes with significant geometrical distortions of the oligothiophene backbones surprisingly exhibited similar electronic structures, indicating insensitivity of interaction with the surface to molecular conformation. Electronic states for annealed ligand-free lead sulfide nanocrystals were investigated, as well as hydrogen-passivated silicon nanocrystals, supported on the Au(111) surface. Delocalized quantum-confined states and localized defect-related states were identified, for the first time, via STS spatial mapping. Physical mechanisms, involving surface reconstruction or single-atom defects, were proposed for surface state formation to explain the observed spatial behavior of the electronic density of states. This dissertation includes previously published co-authored material.