A network mobility (NEMO)-based vehicular ad hoc network (VANET) is a new approach to integrate the NEMO protocol with VANETs. This integration supports communications between roadside units (RSUs) and vehicles and provides Internet access through public hotspots located inside public transportation systems, such as buses, trains, and shuttles. Passengers inside these public transportation systems enjoy full Internet access by using different mobile network nodes (MNNs), such as cell phones and personal digital assistants. However, due to the open nature of wireless network environments, physical-layer attackers can easily localize the MNNs by measuring their received signal strength (RSS) through positioning schemes such as the triangulation scheme. In this paper, we modify obfuscation, i.e., concealment, and power variability ideas and propose a new physical-layer location privacy scheme, i.e., the fake point-cluster-based scheme, to prevent attackers from localizing users inside NEMO-based VANET hotspots. The proposed scheme involves fake-point- and cluster-based subschemes, and its goal is to confuse the attackers by increasing the estimation errors of their RSSs measurements and, hence, preserving MNNs' location privacy. Using correctness, accuracy, and certainty metrics, we show that the fake point-cluster-based scheme achieves higher MNN's location privacy when the number of network grid points in the hotspot decreases. In addition, our extensive simulations show that the fake point-cluster-based scheme achieves 23% and 37% decreases in the average sender's power and the MNN-AP route path length, respectively, compared with the fake-point subscheme.