In the Internet of Vehicles (IoV), roadside units (RSUs) deployed at road junctions enable vehicle-to-infrastructure (V2I) communication and support various intelligent transportation systems (ITS). However, since RSU deployment is constrained by installation cost, determining an optimal placement strategy becomes a challenging problem. Improper placement may lead to insufficient network coverage, increased relay-induced latency, and higher relay energy consumption due to multi-hop vehicle relaying. To address these issues, this paper proposes a learning automata-based multi-objective RSU placement framework, termed LAMP, which jointly optimizes spatial coverage, traffic-weighted coverage, relay-induced latency, and relay energy consumption. In the proposed approach, each candidate junction is modeled as an independent learning automaton that adaptively learns the probability of hosting an RSU using the Linear Reward–Inaction update mechanism. To improve convergence and solution quality, LAMP integrates an adaptive decaying learning rate, a multi-run restart strategy, and a two-phase local search refinement. The framework is evaluated on a SUMO-simulated urban road network of Mangalagiri, AP, India, consisting of 854 junctions, where vehicle arrivals follow a Poisson distribution to represent stochastic traffic flow. Experimental results show that LAMP achieves the highest combined fitness for RSU budgets of 15, 20, and 25 units, outperforming the nearest competing methods by 0.4%–4.2% depending on RSU budget, while requiring significantly lower computation time than population-based optimization methods.