Resource allocation and interference management are two main issues that need to be carefully addressed in visible light communication (VLC) systems. In this paper, we propose a resource allocation scheme that can also handle the inter-cell interference in a multi-user VLC system that employs orthogonal frequency division multiple access (OFDMA). Particularly, we suggest dividing the cell coverage into two non-overlapping zones and performing a two-step resource allocation process, in which each step corresponds to a different level of allocating resources, i.e., zone and user levels. We initially define both zones in terms of the physical area and the amount of allocated resources and we investigate the impact of illumination requirements on defining both zones. Through simulations, we evaluate the performance of the proposed scheme in terms of the area spectral efficiency and the fairness level between the two zones. We show that both performance measures can be potentially enhanced by carefully setting a certain design parameter that reflects the priority level of the users located in the region around the cell center, denoted as Zone 0, in terms of the achievable rate. We further eventuate the system performance in a realistic transmission scenario using a simulation tool.