This paper describes a bioinspired neural-network-based approach to solve a coverage planning problem for a fleet of unmanned aerial vehicles exploring critical areas. The main goal is to fully cover the map, maintaining a uniform distribution of the fleet on the map, and avoiding collisions between vehicles and other obstacles. This specific task is suitable for surveillance applications, where the uniform distribution of the fleet in the map permits them to reach any position on the map as fast as possible in emergency scenarios. To solve this problem, a bioinspired neural network structure is adopted. Specifically, the neural network consists of a grid of neurons, where each neuron has a local cost and has a local connection only with neighbor neurons. The cost of each neuron influences the cost of its neighbors, generating an attractive contribution to unvisited neurons. We introduce several controls and precautions to minimize the risk of collisions and optimize coverage planning. Then, preliminary simulations are performed in different scenarios by testing the algorithm in four maps and with fleets consisting of 3 to 10 vehicles. Results confirm the ability of the proposed approach to manage and coordinate the fleet providing the full coverage of the map in every tested scenario, avoiding collisions between vehicles, and uniformly distributing the fleet on the map.