Hybrid Reconfigurable Intelligent Surfaces (HRISs) constitute a new paradigm of truly smart metasurfaces with the additional features of signal reception and processing, which have been primarily considered for channel estimation and self-reconfiguration. In this paper, leveraging the simultaneous tunable reflection and signal absorption functionality of HRIS elements, we present a novel framework for the joint design of transmit beamforming and the HRIS parameters with the goal to maximize downlink communications, while simultaneously illuminating an area of interest for guaranteed localization coverage performance. Our simulation results verify the effectiveness of the proposed scheme and showcase the interplay of the various system parameters on the achievable Integrated Sensing and Communications (ISAC) performance.