Fast Radio Bursts (FRBs) are millisecond-duration radio transients of mysterious origin, with growing evidence linking at least some of them to magnetars. While FRBs are primarily observed in the radio band, their potential multi-wavelength afterglows remain largely unexplored. We investigate the possible afterglow of FRB 20171020A, a rare nearby and bright FRB localized in a galaxy at only 37 Mpc. Assuming that this source produces a future bright burst, we model the expected afterglow emission in the radio, optical, and X-ray bands under both uniform and wind-like ambient media, within the framework of the magnetar model. Our results show that the optical afterglow is the most promising for detection, but it fades rapidly and requires follow-up within a few hundred seconds post-burst. The radio afterglow may be detectable under favorable conditions in a dense stellar wind, whereas the X-ray counterpart is too faint for current telescopes. These findings suggest that rapid optical follow-up offers the best opportunity to detect the afterglow of the next bright burst from FRB 20171020A, providing unique insights into the progenitor and its environment. To assess observational feasibility, we estimate the event rate of nearby FRBs with sufficient energy to power detectable afterglows, finding a rate of ∼0.3 per year for CHIME surveys. Although this rate is low and the optical detection timescale is short, coordinated fast-response strategies using global telescope networks could significantly improve the chance of success. As more nearby FRBs are discovered, multi-wavelength observations will be essential in unveiling the physical nature of these enigmatic events.