In this study, we demonstrate a general framework for obtaining a plasmonic nanoantenna surface with a broadband polarization-independent response. The plasmonic spiderweb nanoantenna surface is composed of unit cells, which form multiple resonance paths due to patterning of the metallic conductor such that electrons can find multiple ways to oscillate between the poles of the conductor. The tailoring of the conductor paths and shapes of the unit cells' patterns results in a broadband spectral response. At various resonance frequencies, the electrons oscillate along different paths between the poles of the antenna, generating broadband hot spots around those poles.