Task offloading, crucial for balancing computational loads across devices in networks such as the Internet of Things, poses significant optimization challenges, including minimizing latency and energy usage under strict communication and storage constraints. While traditional optimization falls short in scalability; and heuristic approaches lack in achieving optimal outcomes, Reinforcement Learning (RL) offers a promising avenue by enabling the learning of optimal offloading strategies through iterative interactions. However, the efficacy of RL hinges on access to rich datasets and custom-tailored, realistic training environments. To address this, we introduce PeersimGym, an open-source, customizable simulation environment tailored for developing and optimizing task offloading strategies within computational networks. PeersimGym supports a wide range of network topologies and computational constraints and integrates a \textit{PettingZoo}-based interface for RL agent deployment in both solo and multi-agent setups. Furthermore, we demonstrate the utility of the environment through experiments with Deep Reinforcement Learning agents, showcasing the potential of RL-based approaches to significantly enhance offloading strategies in distributed computing settings. PeersimGym thus bridges the gap between theoretical RL models and their practical applications, paving the way for advancements in efficient task offloading methodologies.