For wireless sensor networks, monitoring large inaccessible areas where deterministic node deployment is not possible, self-organized techniques are in demand to cover an area using optimal number of nodes. In this paper, given an initial random deployment of mobile sensor nodes, we propose a simple and novel technique for self-organized node movement to satisfy the coverage of the given region of interest using a least number of nodes, such that the maximum node displacement is minimized. We present a simple centralized algorithm and also a distributed version of it for node placement. Moreover, in case of a node failure, a distributed fault recovery algorithm is proposed to replace it locally utilizing the available free nodes. Analysis, simulation, and comparison studies show that the proposed algorithms with less neighborhood information result in significant improvement in terms of average and maximum displacement of a node, rounds of communication, and number of active nodes.