In the last few years, indoor localization has attracted researchers and commercial developers. Indeed, the availability of systems, techniques and algorithms for localization allows the improvement of existing communication applications and services by adding position information. Some examples can be found in the managing of people and/or robots for internal logistics in very large warehouses (e.g., Amazon warehouses, etc.). In this paper, we study and develop a system allowing the accurate indoor localization of people visiting a museum or any other cultural institution. We assume visitors are equipped with a Bluetooth Low Energy (BLE) device (commonly found in modern smartphones or in a small chipset), periodically transmitting packets, which are received by geolocalized BLE receivers inside the museum area. Collected packets are provided to the locator server to estimate the positions of the visitors inside the museum. The position estimation is based on a feed-forward neural network trained by a measurement campaign in the considered environment and on a non-linear least square algorithm. We also provide a strategy for deploying the BLE receivers in a given area. The performance results obtained from measurements show an achievable position estimate accuracy below 1 m.