The spin light of neutrino ($SL\nu$) is a new recently introduced mechanism of electromagnetic radiation emitted by a massive neutrino (with a nonzero magnetic moment) moving in external media. Although this effect is very weak due to smallness of the neutrino magnetic moment, it can be of interest for astrophysical environments involving compact relativistic objects because its efficiency is higher, the higher the neutrino energy and background matter density. In this note we summarize conditions for best $SL\nu$ efficiency in astrophysical settings and conclude that the most suitable astrophysical site for manifestation of this phenomenon is represented by short Gamma-Ray Bursts (sGRBs) where generation of ultra-high energy neutrinos is anticipated and the matter density can be of the order of the nuclear density. We also give an
estimation of the $SL\nu$ efficiency in the sGRB environment.