Visible light communication (VLC) is currently recognized as a relevant technology for a wealth of possible application scenarios. New classes of services can be designed in both outdoor and indoor environments, exploiting the directionality of the optical channel and the low attainable latencies. Such features allow VLC to offer both spatial localization of users and wireless communication by using widespread high-power LEDs as simultaneous illumination and information sources. In the indoor scenario, one of the most promising deployments is expected in museums, where digital data can be cast by the specific illumination system of each artwork and received by visitors placed nearby. This would enable a full set of services, aiming, e.g., at an immersive experience in the augmented reality approach or at real-time localization of visitors. In this work, we characterize for the first time the performance of a photodiode-based VLC system in a real museum environment, performing an extensive measurement campaign on several masterpieces (wall, canvas, and wood paintings) in the Basilica of Santa Maria Novella in Florence, Italy. In particular, we demonstrate the possibility of using indirect (diffused) illumination light to deliver specific information on each artwork to a visitor. We characterize the quality of such non-line-of-sight VLC links by performing packet error rate measurements as a function of angle and distance from the artwork, and we measure the effective field of view (FoV) of our receiving stage, as well as the influence of side displacements of the receiver on the transmission quality, demonstrating that diffusive VLC links can also be used for efficient localization of users in front of each artwork in museum applications. With observed baud rates up to 28 kbaud and FoV values up to 60° for realistic distances up to 6 m, we believe our work could pave the way for future studies involving VLC in a wealth of indoor applications, beyond the cultural heritage sector.