Considerable evidence suggests that variations in the properties of topological insulators (TIs) at the nanoscale and at interfaces can strongly affect the physics of topological materials. Therefore, a detailed understanding of surface states and interface coupling is crucial to the search for and applications of new topological phases of matter. Currently, no methods can provide depth profiling near surfaces or at interfaces of topologically inequivalent materials. Such a method could advance the study of interactions. Herein we present a non-invasive depth-profiling technique based on $β$-NMR spectroscopy of radioactive $^8$Li$^+$ ions that can provide "one-dimensional imaging" in films of fixed thickness and generates nanoscale views of the electronic wavefunctions and magnetic order at topological surfaces and interfaces. By mapping the $^8$Li nuclear resonance near the surface and 10 nm deep into the bulk of pure and Cr-doped bismuth antimony telluride films, we provide signatures related to the TI properties and their topological non-trivial characteristics that affect the electron-nuclear hyperfine field, the metallic shift and magnetic order. These nanoscale variations in $β$-NMR parameters reflect the unconventional properties of the topological materials under study, and understanding the role of heterogeneities is expected to lead to the discovery of novel phenomena involving quantum materials. ; Comment: 46 pages, 12 figures in Proc. Natl. Aca. Sci. USA (2015) Published online - early edition