Nickel tungsten alloy tapes (Ni—5 at% W, 10 mm wide, 80 µm thick, biaxially textured) used in second-generation high temperature superconductor (2G-HTS) technology were laser-processed in air with ultraviolet ps-laser pulses (355 nm wavelength, 300 ps pulse duration, 250–800 kHz pulse repetition frequency). By employing optimized surface scan-processing strategies, various laser-generated periodic surface structures were generated on the tapes. Particularly, distinct surface microstructures and nanostructures were formed. These included sub-wavelength-sized highly-regular hexagonally-arranged nano-protrusions, wavelength-sized line-grating-like laser-induced periodic surface structures (LIPSS, ripples), and larger irregular pyramidal microstructures. The induced surface morphology was characterized in depth by electron-based techniques, including scanning electron microscopy (SEM), electron back scatter diffraction (EBSD), cross-sectional transmission electron microscopy (STEM/TEM) and energy dispersive X-ray spectrometry (EDS). The in-depth EBSD crystallographic analyses indicated a significant impact of the material initial grain orientation on the type of surface nanostructure and microstructure formed upon laser irradiation. Special emphasis was laid on high-resolution material analysis of the hexagonally-arranged nano-protrusions. Their formation mechanism is discussed on the basis of the interplay between electromagnetic scattering effects followed by hydrodynamic matter re-organization after the laser exposure. The temperature stability of the hexagonally-arranged nano-protrusion was explored in post-irradiation thermal annealing experiments, in order to qualify their suitability in 2G-HTS fabrication technology with initial steps deposition temperatures in the range of 773–873 K.