We investigate the propagation, attenuation, and localization of nonlinear elastic waves in a 1D granular crystal using high speed photography. We measure temporal displacement profiles of individual particles with a micrometer-scale resolution, and we reconstruct force profiles of propagating solitary waves and localized breathers by synchronizing and analyzing the acquired data. These investigations provide quantitative evidence for the transmission and attenuation trends of travelling solitary waves in a soft polymeric chain, which are significantly different from those in a hard metallic chain. We additionally study energy localization in a chain of hard particles embedded with a soft polymeric impurity. Specifically, we show that the proposed experimental technique is able to visualize the formation of localized breathers and quantify the energy highly concentrated in the vicinity of the impurity site---a phenomenon which can be exploited for harvesting vibrational energy in engineering applications. Finally, we compare, with good agreement, the experimental results with discrete element numerical simulations that account for dissipative effects due to viscoelasticity. The findings reported in this study imply that high speed photography can be an efficient and effective tool for non-contact measurements of nonlinear wave dynamics in granular lattices, despite their short characteristic times and minute displacements.