Nowadays, sensor/access-point coverage is an essential problem for wireless communication and sensor systems, which will significantly impact the quality of access, monitoring, and surveillance. Indoor sensor/access-point placement still remains very challenging as the regions of interest (ROIs) or underlying geometries may be in an arbitrary polygonal shape. In this work, we would like to study how to place a sensor/access-point to maximize the coverage area within an arbitrary polygonal ROI. Our novel approach is based on finding the maximum-area clique over the visibility graph corresponding to the indoor geometry. According to many examples, our proposed optimal sensor/access-point scheme can lead to larger coverage efficiencies than the existing solution to the art gallery problem (AGP) and the conventional Delaunay triangulation method. Our new scheme is of great practical value as it can be applied for not only both convex and nonconvex simply-connected polygons but also both convex and nonconvex multiply-connected polygons with internal holes.